Ditto on principle if seller would not allow gunsmith to view gun even in his presence that you both know. However there are lots of old guns bought and sold with no problems without a hosford gauge being involved. You indicated that there were no glaring issues and everything looks worn correctly and lightly used so what makes you think you need a hosford gauge. It sounds low risk to me.
I think on this one like most purchases involving even moderate conspicuous consumption, mind justifies the heart and ultimately it depends on the significance of lady friend shooter. Good luck with that decision. BTW post pictures of gun when you get the chance.
Just kidding.
My guess is if that was not even a slight consideration you would have moved on without second thoughts if gun was just for you. I call these AMFYOYO moments if indeed gun for you is only consideration. However, the gun fits her and your justification is that it could be a back up to back up another gun, which may be well worth it. Have heard of back up guns having issues on big trips. If you like shooting old guns, they sometimes have issues and leave you hanging so having many options is my justification. Other justification for you is that with that shorter stock that could be your cold weather gun to account for when your all bundled up with a heavy coat that shorter stock will fit nicely.
Seller has basically indicated he doesn't need to sell it based on his - my price and my terms posture but that short stock could cause him problem. It is still a needs based negotiation though. Rarely in a fairly common commodity does a seller or buyer get both sides of the equation.