There is a clear connection with the present. Even though the meeting itself occurred a few days ago, information is still relevant. At the moment of speaking Brain is still at university, he's studying psychology and enjoying it.
As for the last cue, the word says here is more about Brain's attitude towards the course than the mere fact he said something (as @JavaLatte mentioned in their answer). Likewise, at the moment of speaking he still thinks the course is good.
(said would sound formally correct, too, but so long as present tense is used before, says is more natural)
However if the meeting with Brain had happened a long time before the dialog, information might not be relevant anymore and past tense would make more sense. Compare:
"I saw Brain a few years ago."
"Oh, did you? What was he doing?"
"He was at university"
"What was he studying?"