I think it's a mix:As expected, this was either (a) Mayfield's agent straight-up lying to make his client seem better and more in demand to counteract all the criticism the Browns were getting or (b) subterfuge by the Patriots in the hopes that Mayfield's agent would blab to the Jets, etc. and get them to give something up to move up to #2 for no reason (or, possibly, just a lame attempt to convince Mayfield to work out for the Pats).
The Patriots did want to work him out. CHECK
The Patriots had the ammo. CHECK
The Giants did say they received calls. CHECK
The agent I don't think ever said the Patriots actually called the Giants, he said there might be a surprise team.