At least in 2010, it was not so.
You have to be an administrator only to approve administrator approved forms.
These are usually the form templates with external data connections (and/or heavy code behind) requiring Full Trust and code signing with a certificate
And, as far as I can judge from my experience in Office 365 (Sharepoint 2010 Online), the latter could be frequently avoided by converting data connections to UDCX connection files stored in data connectiion library on the same sharepoint site collection