Rimini Street, or anyone else for that matter, shouldn't be touching standard code, although theoretically they could with the appropriate object key. Getting an object key wouldn't be easy, as if you are off support then you can't use the SAP Support Portal where you would normally request access.
SAP would advise against going off support and using a third-party support provider.
Perhaps a better solution would be to take a look at what you are paying support for, and what you are getting in return. A lot of customers don't seem to take advantage of a lot of the support offerrings, so maybe if you were getting better return on your investment your boss would feel better about paying the annual SAP support bill?
There's a useful website with information about third-party support providers: http://www.offsapsupport.com.