See
Computer Trades for a lengthy thread, mostly regarding computer-to-computer trades.
While I do not know exactly how it intiates offers to human-controlled teams, you are exactly right when you say that the AI does not consider it team much, if at all, when making trades and free agent signings. The AI does a very good job of evaluating individual player value, and the trades it makes are usually balanced in overall value on both sides, but make no consideration for the value
to that specific team...For example, say Derrek Lee has equal value to Carlos Beltran. A team might trade Lee for Beltran, even though it has an outfield of Carl Crawford, Grady Sizemore, and Vladimir Guerrero. The trade looks good because it has equal value on both sides, but no consideration is given to the fact that Beltran is not valuable to that team becuase there is no place for him to play.