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?"
"Psychology"
etc
3So can I say John says he's really like pizza? Because it's expressing an opinion what he still holds, that's right? – Lai32290 – 2017-04-11T13:11:13.130
7@Lai32290 Fixing the typo ("John says he really likes pizza"), yes, that sounds fine to my ears. ("John says he's really like pizza" makes sense if you wanted to mean that John claims that he is similar to pizza!) – Muzer – 2017-04-11T14:06:55.873
For such recent speech, about a course Brian is still enrolled in, you can use "is a very good course" even for reported speech, and even with "said." It's still current information, and the course is still in progress. If you're having this conversation 6 months later, then past is more appropriate. – Karen – 2017-04-11T17:09:05.017
@Karen: I agree about the backshift for is not being essential, and have updated my answer. As I have already stated, says indicates that Brian probably still holds that opinion, and has nothing to do with whether the course is still in progress. Note the present says in this sentence: "He says that his student days were the best years of his life". This is his current opinion, not reported speech- even if he told you several days ago. – JavaLatte – 2017-04-11T17:37:52.490
This is also the basis of the joke "depends what the definition of 'is' is." – fectin – 2017-04-11T17:38:23.280
1
@fectin: That was no joke, that was a president defending himself against perjury charges. https://en.wikipedia.org/wiki/Impeachment_of_Bill_Clinton
– JavaLatte – 2017-04-11T17:46:33.260And that specific line was a joke: https://www.youtube.com/watch?v=Yp3TQf2xDc8
– fectin – 2017-04-11T17:52:06.883