The short answer is "Yes" it is legal to not report. There is no obligation to report to the credit reporting agencies.
It is unusual but some local banks still don't report.
You are doing the right thing by talking to them - I would continue to ask them to please report this account (assuming you are current) and in the meantime the payment history might be helpful. The credit reporting agencies don't have to do anything with the payment history you send but it won't hurt.
I hope this will all work out for you very soon!
PS - if you found this helpful, please check the box below - thanks!