Lyle's Jurisdiction

Lyle is an Arizona sheriff. Shouldn't his involvement in the plot end the second the convoy enters New Mexico?

In Smokey and the Bandit, Buford T. Justice pursues the Bandit way, way out of his home state, but the plot makes it clear that the other characters consider this highly unusual. Other law enforcement officers clearly want nothing to do with him, and he's only able to assert himself over them and become involved due to sheer force of personality.

Lyle... is just sort of there. He goes where he wants, when he wants, with no argument from New Mexico or Texas cops at the county or state level. Even the Feds in the helicopter have no visible issue with him tagging along. Is there a scene missing where he's granted some kind of special powers? Because unless there is, then an Arizona cop running around New Mexico and later Texas with no objections from cops in those states seems really weird.

I mean, really, how many times will you look under Jabba's manboobs?