If you WERE an ally - IE, a diplomatic envoy of a friendly foreign power - you absolutely would be allowed access to their lower security facilities.
Um... no you wouldn't. Not automatically at least, and definitely not just by rocking up and saying "don't you know who i am?"... more likely you would
cause a diplomatic incident by rocking up unannounced. Just allowing access based on who someone is[1] is how junior security guards get sacked.
But additionally, i think you over-estimate what "Allied" means here. You're nothing more than a mercenary with a solid, established reputation for getting the job done... a preferred contractor if you will. And like any contractor.. you don't have business at my facility? You don't get access.
You still aren't part of that (minor) faction, nor granted any special privileges other than system permits (which might as well be no access anyway) and the ability to purchase specialised hardware... but even that is only at the superpower level.
Leaning harder on that "diplomatic incident" piece though... I'd rather see reputation become a commodity, lost to "purchase" services like:
- temporary level 1 access to a related facility, like you suggest here
- clearing a level of notoriety
- gaining access to "surplus/ reserve" cargo stores where a market might be cleaned out
- requesting specific mission types.
All these can be realised as you putting the hard- pressure on your contact, who ascedes to your demand, albeit begrudgingly.
EDIT: Heck, let's just throw outright bribery into the mix. Dark universe and all that jazz.
[1] and not their authorisations/appropriate documentation