1) The tree appears to be a willow, of which some species are native to
Arizona, the largest of which is the Goodding's Willow (Salix
gooddingii) which can grow to 45 ft in height.

Yes, but ... the tree is already 50'.

2) A neighbor must have complained about the tree.

Most likely, true. But "busybody" towns often send employees around
looking for something to write up.

As a matter of practicality, it doesn't matter whether it was a neighbor
or a town employee.

3) Municipal bylaws concerning existing structures are generally not
retro-active.

That's tricky. But, usually true. But a tree isn't a structure. Or,
if you wish to consider it a structure, by growing it's "modifying"
itself. Changes to existing structures often have to meet current
standards.

4) The guy appears to work in the health-care field, so he might have
deep enough pockets to fight this in court.

Like it or not, communities have the "police power" to regulate such
things as permitted vegetation. This often comes up when an owner
decides to stop mowing his lawn.

Frankly, that tree hardly looks like any desert tree I have ever seen.
It's clearly "non-native" and likely is thriving because the owner(s)
have been watering the lawn.

But it just doesn't look right for a town built in the desert. (Green
grass golf courses in the desert don't 'look right' either but ...)

I didn't download the video, but from my "Eastern" point of view, 50'
high trees less than, say 40' away from a house are accidents waiting to
happen. Take the damn tree down and for $1k be done with it.

Look at the bright side: in some areas, you need a permit before you
can cut down a tree.