I got a Mortarboard badge due to a bounty I received today. The definition of the Mortarboard badge is to have gotten the max rep for one day, but the FAQ states that bounty does not apply to the 200 daily rep limit. So technically, I haven't reached my daily limit, yet I still got the Mortarboard. I can understand why the system awarded the badge, but it doesn't seem entirely correct... does it?
The bounty will always be awarded even beyond the rep cap (in that sense the bounty doesn't apply to the rep cap),
but afterwards, you won't be getting any more rep. In other words, upvotes before the bounty are awarded, upvotes afterwards aren't.* So you have reached the rep cap for today, hence the badge.
*This is not true anymore; bounties and rep cap have been fully independent for a while now.
Actually, any rep you earn via any means, up to the first 200, counts toward your rep cap. Hence your bounty most likely put you at or over 200 for the day, and you have effectively rep capped.
The difference with bounties (and acceptance in general) is that they are immune to the effects of the rep cap. That is, at 200, you get nothing for upvotes -- but acceptances and bounties will take you over the 200.
This is how the legendary Jon Skeet averages over 200 per day.