My personal feeling on the matter is that they have Gutierrez on speed dial, ready to sign in case of an emergency start, and they have a gentleman's agreement with Culpepper that he will be signed in the event of an emergency as long as he has demonstrated a healthy knowledge of the playbook and the offense they run.
I know this sounds completely off base and it is wholly unfounded, but hear me out. Culpepper is undoubtedly a talented player. He is a physical specimen at quarterback, the type of athlete every general manager is looking for at the position. Six feet four inches, 260 lbs, a cannon for an arm and the type of mobility that makes him a threat to run in the event of a broken play. The knock on him, and most likely the reason he is still out of the league, is an inability (or unwillingness) to grasp the small nuances of the game. He struggles with taking what is given and forces unnecessary mistakes down the field.
Most of the league has caught on to this fact (that is why he is still unemployed, despite the not untrue notion that, athletically, he can still string 'em up). By retiring, he has accepted that he can no longer make it in the league as things are presently constructed.
If I were Bill, I'd send Culpepper a portion of the playbook to determine whether or not he is either motivated enough to put forth the mental effort necessary to succeed or to see if he can even do it. Culpepper's motivation in this instance is that, in the event of an injury to Cassel, he will have an opportunity to start for an NFL team. Not just any team, at that, but one with a wealth of offensive and defensive talent that is ready to play at a championship level.
The odds of him signing with another team are slim at this point and would be absolutely nothing-at-all if he has agreed to this type of situation.
It's a potentially win-win situation and makes sense on the Patriots part because they don't have to devote a valuable roster spot to a third quarterback.
This would also explain why they turned away Tim Rattay and Chris Simms at such a short notice and is plausible if Culpepper contacted the Patriots on his own (I don't see why he wouldn't make such an attempt).