Agreed. When these free agents get signed right away, its wrong to assume it means there was no other interest. The Bills laid out a good offer immediately when the clock hit 12, and his agent probably got on the horn to see if anybody else would outbid those numbers. Once he finds out this is the best he's gonna get, there's no reason to delay. Doesn't mean nobody else wanted to sign him.
Guess we'll have to agree to disagree. If there was more interest, the Bills would've had to go higher. If there were less, they could've gone lower. I think the eventual contract gives you a pretty good idea of the demand for the player around the league, except in cases where a team grossly overpays, like Washington and Oakland have done in recent years.