It is a sticky spot legally, and there are rules they have to follow. But this man has experience doing high-risk repos that public law enforcement doesn't have. It's the difference between regular infantry and mercenaries.
I can't speak to property seizure warrants, so you may be right there. However, if it is anything like arrest warrants, this is rarely true.
Fun fact: Typically, it takes a mountain of evidence to convince a judge to issue a warrant, and then those serving the warrant have a small window of time to execute. If they are late, or the individual isn't present, then it expires and a new set of evidence has to be presented to issue another warrant.
(I often think it's amazing anyone is arrested at all).
My lack of knowledge notwithstanding, I doubt that issuing a warrant to seize a plane would be a quick, Law and Order-like process, simply due to the size and dollars involved.
Most of the time they just fill out the paperwork and go get the plane. But getting the paperwork straight and finding the thing are really hard to do unless you've got a good team of experts ready on a moment's notice. Which he has. But that would make for boring TV.
There is some reason that they can't or won't just ask the police to secure the plane, though, and my guess is that the reason is more that it's legally unclear whose plane it is. That is, in some cases, this is legally just theft that's papered over later.