Do I have the wrong perspective here?
To an extent, yes. It can be very difficult for a non-technical person to discern whether something they have is well-constructed or barely-holding-together junk. For example, I was part of a team that was requested to look over a large codebase for a Photoshop-like product that was being sold off by its owners in the late 1990s.
However, I can understand your hesitation. You've done some work and are producing value for them and don't want them to look over your code, steal the core ideas, and make their own product without giving you anything. That's a legitimate concern.
So what to do? Would it be possible to find someone that both of you trust for the review? Someone whom you could be sure wouldn't just look at your code and do a trivial rewrite of it, but whom they could trust to tell them whether it's reasonably maintainable code? If so, that might be your best bet. If not, you may be at an impasse.
Look at it this way, if you did let them review it and they stole your ideas and rewrote it with their own code, what would that cost you? You've done the work for free already. Can you resell it to another customer? If they review it and find it not to be to their standards, but don't rewrite it themselves, you'll be in the same position.
In the comments you ask:
I guess following that logic, he should be fine with me finding an MBA to grill him on his business acumen.
Yes, absolutely! You should know who you're doing business with. Check the Better Business Bureau to see if they have any complaints filed against them (if you find the BBB to be useful). Certainly ask an established entrepreneur you know to vet their business plan if you're concerned about their ability to pay you in the future. It's called due diligence and is a widely accepted business practice. If you don't do it, there may be cases where you have nobody to blame but yourself for not getting what you expect out of the relationship. (I've been there! It's not fun.) Good luck!