Thais are schooled with perfect handwriting.

With the extreme pace the technology is advancing (and with Moore's law still proving to be pretty accurate/valid), handwriting will be a completely obsolete skill within not many years. There is no reason to spend hours upon hours each month teaching students to perfect it, other than the fact that it promotes other useful skills like concentration and thoroughness, has sentimental value even when obsolete and possibly so we'll be able to read handwritten letters from the past.

Many would argue it's already an obsolete skill in most first world countries.

My hand writing is terrible, as are most of my friends. I have trouble reading my own writing at times.

My wifes hand writing is perfect, as are her friends. Actually, I have never seen a Thai with bad writing. The older Thais have very tidy writing. Even the younger ones that like to add the odd artistic squiggle or trendy floral design to their writing have lovely articulate script. Hand written receipts from the local hardware shop could be framed.

Is it because of their fine dexterity? Their education? Or some other reason?

it isn't true, seen loads of bad writing