I agree with the previous posters. Go with your gut - what you describe sounds absurd. And our daycare have gotten kids whose first language was *not* English, and even then, they don't focus on penmanship at all regardless of what your native language is. For children with difficulty with English, they would really emphasis talking and listening - writing correctly at 3 is not on their radar, not even for kids who are native English speakers. So, in a nutshell - I would not back up the teacher at all. If he wants to write, it should be fun. Not work, not something to be corrected.
DS4 was in a traditional preschool/daycare at 3 (lots of play with early intro to some things) and even there, the teachers never corrected or pushed him on getting correct letters. They would ask "do you want to practice letter X today?" and more often than not, DS would say no, and take off for a play center, and the teacher just left it alone. He never came home with any worksheets although he came home with plenty of artwork. So while we saw some other kids with lots of writing examples, his was sparse - and his teacher never said anything about it at all to him or us because frankly, it is NOT important at 3. They emphasized more social skills and listening.
Heck, even now, being in a GT class at age 4, the few worksheets he brings home are full of his writing attempts - mixed cases, letters backwards at times and even a few with just a few letters of his name. And even then, his teacher does not cross anything out or call him out on his size or mistakes - they emphasis the fact that he keeps trying and never gives up, not whether it is correct and because of that, he is actually enjoying it all a lot.
