They get to use the player's resources through training/researching/whatever, but they don't get the direct control over it.
For example if player 1 has full shared control with player 2 then p2 can use p1's gold to train a footman.
Ghan has said he has fixed this. Monovertex please confirm this fix. This was only a problem with people that had signatures in the upper levels like not the special members but the respected members.