It's entirely up to him, if he's more comfortable not disclosing then fair play to him. He's shown a clear progression since then and could argue that he wasn't ready for university the first time round, but as a more mature individual now, he feels more comfortable to cope with the demands of full time study.
Personally, I would disclose, if only for the simple fact that it justifies his grades at the time. It's not something to be ashamed of, it's just one of those things. I think that even though he doesn't suffer now, having the support staff aware of his past history might be beneficial in case the stress of uni life causes a relapse. There is always the possibility of disclosing at a later date too, so the option is available should he change his mind and wish to take it.
As for the evidence, I'm fairly certain something will be required, but it might not even be anywhere near as formal as a medical note that explains his medication's impact. Maybe his reference could pop a few sentences in that state the circumstances for his poor grades at the time, but reinforce his merits, progression and talents since then? It will be more complicated justifying his grades if he's not disclosing because of it being a medically-related mitigating circumstance, but again, that's something for him and his reference to look into.
I'd still suggest contacting the uni's he's interested in like I've already mentioned, even if it's only to ask from a purely hypothetical standpoint as an anonymous user. At least then he'd know if it were worth his while to disclose or not.