But even if Carl and Russell turned out to be black market bird dealers or something, Muntz could have easily negotiated an arrangement with them, since he only needed the bird temporarily (that is, long enough to show it to the public). He was only making things harder for himself by antagonizing the only people who actually knew where the bird was.
And they brought along their entire kitchen as a warning.
Even if he was afraid Carl would take the bird to civilization and claim credit, he didn't need to worry -- all that would do is vindicate Muntz's discovery from 70 years earlier (remember, he had a skeleton of one -- he was unquestionably the bird's discoverer). Also, at one point Russell casually tells Muntz about the bird's weakness for chocolate bars (literally the only reason it befriended them) and he does exactly nothing with this information. It would have made a lot more sense to rig a few chocolate-laden traps, sit back and wait for the bird to wander into one.
"I don't understand. When do the flying dogs come in, exactly?"