Just from topic title, I was gunna suggest getting the car inspected at a neutral shop where neither of you know any employees. Thought it was an issue of hiding broken/failing parts. In your situation, I'd just be honest. Say "I have the funds to buy the car, I want to see it (and have it looked at by gearhead, if you aren't super knowledgeable about car stuff). Can I look at it/have a random shop check everything?"
If they refuse, they're selling a stolen car, trying to scam someone on a lemon, or impatient and immature. In any of those cases, it's not worth your time or well-being. If there's nothing to hide, they shouldn't have any issue getting the car checked up at a shop.