Don't think I've ever seen that, but I would assume that it could happen if the team had players on the 60-man DL at rollover, and the 40 was already full.  After rollover, those DL'd guys are back on the 40.

Yeah its new to me as well. 

I got 41 or 42 players on my 40 Man once.  I don't recall exactly how it happened, but I'm pretty sure it was a combo of players coming of the DL, accepting options, and/or arbitration signings.

My best guess was that anything (or at least 1 thing) I did that didn't require pressing the Submit Pending Moves button on the Roster Mgmt got me extra players on the 40.

Your guy with 45 will probably be able to sign FAs, but he won't be able to assign them to any roster.  He won't be able to promote or demote.  He can probably make trades, but he won't be able to assign the players he gets.

Probably an advantage going into the Rule 5 draft. But he won't be able to pick up any players, so it could be he's got some crap players on his 40 and, if he has a high pick, he'll be missing out on a better player.  Assuming he has any moves to make at any level before the season starts, he's going to have to fix this soon. The players coming off the 40 will probably have to pass waivers, so he'll lose them if they are any good.

I think he'd be able to assign players that have options to the minors.

He will.  I've got 40 on my 40 in Coop.   At the end of FA, I signed a couple of players with options for insurance.  They'll be sent to AAA and added to the 40 if an injury occurs.   Barring that, I'll designate a couple of guys on the 40 with options and add these two before roster expansion.   Then release them at season's end to put the designated guys back on the 40.