What you're saying makes sense and is grounded in reality. Unfortunately, the spygate truthers have already come up with an alternative to this: They believe that the Patriots installed a second radio frequency in Brady's helmet that allows him to hear instructions after the 15 second cut-off.
The "smoking gun" behind this claim is a comment that Doug Flutie allegedly made to John Saunders and Saunders told to Dan LeBetard. The story is that Flutie, while with the Patriots, picked up what he thought was his helmet, but was actually Brady's backup helmet. He could hear Brady receiving information about what the defense was going to run.
In the original story, there is no mention of this warning coming after the 15 second cut off. Also, no one has apparently spoke to LeBetard, Saunders, or Flutie to confirm any of this. For the truthers, they don't need anything else. In their minds, that's indisputable proof, despite the lack of anything to corroborate or substantiate that story.
In addition to the lack of any evidence (Why hasn't the NFL noticed during their regular or random electronic sweeps over the last 15 years? Why hasn't any other backup QB noticed this?), this story also fails from a common sense standpoint. The back up helmets for the offensive and defensive signal callers (the green dot helmets) don't just sit around in the bench area. Those are kept in a trunk and in possession of a league employee until they are needed. The teams can't access them.
Also, pretend for a moment that this story is true: If the Patriots were doing this, why would they leave the one piece of physical evidence that could reveal their entire scheme just lying around, unattended, for anyone to pick up? And why would Flutie, after discovering this, decided to only mention it to a media member in passing and not, for example, got to the league?
So, yeah, you're point is correct. There's just a lot of misinformed, gullible, and envious people out there.