Is the student younger than 13? Google does not allow gmail accounts for individuals younger. Perhaps this will help:
https://support.google.com/accounts/answer/1350409?hl=en If age is not the issue; perhaps have the student create a new gmail account? Google does permit multiple accounts I think.
MIT has no control of restrictions imposed by Google regarding Gmail accounts. I am not aware of any MIT restrictions blocking any valid gmail users. Google is merely adheres to legislation intended to protect minors in many countries. Why this account has issues may be due to restrictions imposed by Google for other reasons. If the student cannot send/receive eMail (indicating the account is probably active), it would appear Google is blocking access. ..and only they can explain why. A valid account is MIT's only requirement and this requires a valid Gmail account.
Please let us know how you resolve this.
Regards,
Steve