Surely they don't expect her to submit the original document? That would be very unusual. You normally make a copy or a scan and send that. What's important is that it's translated. Make sure that names are spelled correctly in the translation and you shouldn't have a problem.
If there is a problem with the actual birth certificate then that will be a problem to resolve. She will have to go back to the office that originally issued it ('Amphur' office, that's the district level of governance, they handle the civil list) and take both certificates and her ID card. This kind of thing is not normal procedure so different officers will tell her different things on different days and, yes, there may be a fee (above the table or otherwise) to get it cleared. She'll need to be patient and may need to go several times. On the other hand she may get lucky and have it done in 5 minutes.
She should do it though as it could cause problems in the future.
I have known someone whose family name written in Thai on their birth certificate bares no resemblance to its official English translation. They simply make sure any translation of it bares the correct English spelling and that is accepted by governments around the world. Trying to get it changed would require new housing registration, ID card, passport, bank accounts, basically a whole new identity.