I was checking out a few fender guitars at a local pawn shop,

and I found a strat and a tele. Both of them had their string trees screwed ALL THE WAY down, almost to a point where the two tips of the butterfly string tree were touching the headstock.

I've never seen a guitar set up like that, but is that an acceptable setup?

If it is wrong, can it be fixed?

My 2009 Standard Strat has a single string tree on the B and E strings. It is screwed all the way down to the headstock. I would have to look, but I believe that is the case on all the other Standard Strats I have seen.

I also believe that on the models that have two string trees (butterfly type), the one on the D and G strings is on a post slightly higher than the B and E tree.

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2012 American Standard Strat Charcoal Froast
2009 Standard Strat Sunburst Brown
Blues Junior Tweed NOS
2007 Line6 Spider Jam

Everything on a guitar is about physics.

On a Stratocaster off the back of the nut you need to have a string angle of approx 12 degrees for the low E across to 5 degrees to the high E where it winds onto the tuner post.

There are two reasons for this. First is to ensure that when using the trem down the string doesn't pop out of the nut. The other is that the string breaks across the nut correctly and reduces the chance of buzzing.

String trees are just to ensure that the string can make that ballpark angle.
The problems start when you have low string tree and the last winding on the tuner is higher than contact point on the string tree.

This may cause damage to the tuner especially if the tree is a non roller variety as you are exerting extra force winding the string through this bend. The more acute the string tree angle the higher risk of breaking a string there.

It might slightly affect tuning stability if the tree is grabbing the tree and when a bend is played the string moves. This would be more apparent the further away the tree is from the post (which is why its normally a nut issue).

Ideally if you need to use the string tree at all you want the string to come down off the nut and through the tree to the tuner post with as little bend in it as possible.

If the tree is really low in relation to when the last winding on the post is you can. Bend the wings slightly higher. Replace the tree with something more suitable or use a longer suitable screw.

So there is your answer. Where does it wind on the post, how hard is it to tune, does it snap strings, is tuning stability a problem on those strings.
If none of these problems are apparent then its fine.

Specifically on a full height tuners, non string locking tuners I tend to put enough string on the high E string for 6 winds which gets it down near the height of the tree or sufficiently low enough to make the 5 degree angle.