I just ran into this issue, and in fact do have a keyboard and mouse connected. I was able to stop the behavior by disabling and re-enabling Screen Sharing in System Preferences. I don't think I had a mouse plugged in at system startup, so my guess is that it just checks for keyboard/mouse presence at launch, and behaves according to that initial state.
So, for those having the issue where a kb/mouse aren't present, it may be worth it to try plugging a kb/mouse in at startup then disconnecting them, and seeing if it persists, just to pin down if that's the determining factor.
A little annoying to say the least -- this should really be a checkbox in the Security or Screen Sharing preference pane.