Larry, VJax and Wallace were available and dismissed, even Sanders and Cruz were available.
To me the issue is applying a baseball mentality to the NFL game. If I am wrong I apologize, but I do see this phenomenon quite a bit. Building an NFL roster is not the same as the Red Sox or Yankees going out and procuring whatever players they so desire.
For example Larry Fitzgerald was never available because of the NFL salary cap. If Arizona traded him they would have taken on a huge cap hit, with all the pro-rated signing bonus being accelerated into the current season. Trading him would have hurt their team immensely, without even considering losing him as a player.
Vincent Jackson signed a $55 million contract. Tampa Bay was able to make that deal because prior to that in the uncapped year they took advantage of their being no salary floor, and as a result had about $40 million worth of cap space to play with. Competitive teams such as the Patriots did not have the flexibility to match that offer.
Similarly Mike Wallace signed a $60 million contract. Teams that already had high priced quarterbacks are unable to make that kind of a deal feasible, so teams like the Patriots, Packers, Steelers, Broncos, Giants, Ravens, etc. had no chance of signing him.
Victor Cruz was a restricted free agent so a team signing him would not only have to beat the original team's offer, but in addition trade away a draft pick. It is extremely rare for any RFA to sign with another NFL team; this isn't something that applies strictly to the Patriots.
The salary cap and free agency make roster building and retention a very difficult endeavor in the NFL. It is quite unique in comparison to MLB and other pro sports.