Personalities of the Buddhist Suttas
 At the top, Beggars, of those of my Female Upasakas who realized faith as a consequence of overhearing the word being passed along [not a great translation, I admit! This is really the word which describes the way we are all here picking up the Dhamma, by word of mouth, not by learning face-to-face with a master] (anussavappasannanam) is Kali upasika Kurara-gharika.
Kali upasika Kurara-gharika
(Called Kururagharika, described among laywomen as the best of those who believe even from hearsay (anussavappasannanam). She was the mother of Sona Kutikanna, and her husband belonged to Kururaghara in Avanti. When with child, she came to her parents in Rajagaha, and there, while enjoying the cool breeze on the balcony above her roof, she overheard the conversation which took place between Satagira and Hemavata on the excellences of the Buddha and of his teaching; as she listened, faith in the Buddha grew in her and she became a sotapanna. That same night Sona was born. Later, Kali returned to Kururughara and there waited on Maha Kaccana. When Sona entered the Order under Kaccana and visited the Buddha, she gave him a costly rug to be spread in the Buddha's chamber. When Sona returned home after this visit, Kali asked him to preach to her in the same way as he had earlier preached to the Buddha, earning the applause of the Buddha himself and of the devas of the ten thousand worlds.
Kali was considered most senior among the women who became sotapannas. She was the constant companion and staunch friend of Katiyani.
A conversation between her and Maha Kaccana is related in the Kali Sutta.
From: PTS, Woodward, trans., The Book of the Gradual Sayings, The Book of the Tens
Once the venerable Kaccana the Great was staying among the Avanti at Kuraraghara (Ospreys' Haunt) on a sheer mountain crag.
On that occasion the lay-follower Kali came to see the venerable Kaccana the Great, and on coming to him she saluted him and sat down at one side. So seated she said this to him:
'Sir, this was said by the Exalted One in The Maiden's Questions: (Footnote: Answer to the question: 'Why makest thou no friends among the folk?' of the personified Tanha at S.i., 126; K.S.i, 158.
On winning of my weal, my peace of heart,
(Routing the host of sweet and pleasant shapes)
Musing alone I have attained to bliss.
Therefore I make no friendship with the folk.
Friendship with anyone is not for me.
Pray, sir, how is the full meaning of this briefly put saying of the Exalted One to be viewed?'
'Some recluses and brahmins, sister, highly expert in the attainments of the earth-device, have wrought their weal thereby. But the Exalted One has thoroughly comprehended to its utmost reach excellence in the attainment of the earth-device. By thus thoroughly comprehending it the Exalted One saw origination, saw the danger, saw the escape, saw the knowledge and insight into the Way and Not-way.
Some recluses and brahmins, sister, highly expert in the attainment of the water-device ... the heat-device ... the air-device ... the blue-green ... the yellow ... the red- ... the white ... the space-device ... the intellection-device [the Dhamma device, the device those of us here are using ... we can hope], have wrought their weal thereby. But the Exalted One has thoroughly comprehended to its utmost reach excellence in the attainment of the intellection-device; thus thoroughly comprehending he saw the origination, saw the danger, saw the escape, saw the knowledge and insight into the Way and Not-way. As a result of so seeing, the attainment of his weal and peace of heart were seen by him. Thus, sister, as to what was said by the Exalted One in the Maiden's Questions ... this is how the full meaning of the Exalted One's briefly put saying is to be viewed.'
Footnote: Edited from a Discussion of this Sutta:
MO: I believe that for purposes of this discussion the Woodward translation is sufficient.
First, let us establish the context: This sutta is the explanation by Kaccana the Great to Kali of a sutta uttered in brief by The Buddha.
Second, I believe it is safe to say that the phrase "As a result of so seeing, the attainment of his weal and peace of heart were seen by him." Is sufficient to explain why "friendship with the folk, or anyone," is not for the Buddha: It is not through friendship with the folk or anyone that one's weal and peace of heart are attained. [That is, for the Buddha! For the rest of us, friendship with the folk can be foregone, but friendship with the wise is something we would do well to cultivate.]
My statement that: "It is easy to see this sutta as a discussion of the various kasinas, or concentration devices; I think this was just Maha Kaccana's way of describing 'friends' or the ways of practitioners of other systems." Was intended to explain why Maha Kaccana chose to explain why friendships were not for the Buddha by way of explaining the Kasinas. In other words, he took this long way around not to talk about the Kasinas, but to show Kali that "Folks" would all fall into those who attained their satisfactions from one or another of these disciplines and that the Buddha had encompassed and surpassed these and found his satisfaction in the solitary practice of meditation.
Robert: "One aspect suggests the limitations of concentration meditation. That it is still tied to the world, still Dukkha. But the Buddha has fully understood all these meditations and seen them through vipasana insight and the noble truths."
Here the text would not support this argument. It states: " ... thus thoroughly comprehending [the kasinas] he saw the origination, saw the danger, saw the escape, saw the knowledge and insight into the Way and Not-Way."
This indicates that it was a consequence of his mastery of the different kasinas that he attained his knowledge and [again the word here is not vipasana, it is dassana, seeing] insight into the way, not that he has seen the limitations of the various meditations through knowing and seeing and the Way.
Finally, I am not sure what you have in mind when you speak of concentration meditation. While the kasinas are called in translation "concentration" devices, and their initial use is to enable concentration by focusing the mind on a single object, the nature of that object is always universal: Earth, Water, etc, such that an utterly encompassing comprehension of the device is (in it's broadest sense down to it's deepest roots), (like the "Lessons" given in The Course here), sufficient to lead one to the Goal. In the sutta in brief, the kasinas are not mentioned, what is being spoken of is Jhana, or Burning, which is classified under Samadhi, which is sometimes (I believe erroneously) translated concentration. Concentration (one-pointedness of mind, focus) is an aspect of the Burnings, and therefore of Samadhi, but Samadhi is not limited to concentration. [In the phrase "A Man of View," in the following, "View" is, "Ditthi" and goes beyond the meaning I usually give to this word, that is, hypothetical view, or opinion. This clearly is the attainment of one who knows and sees.]