I have run into requests like these twice.
First time the big gorilla company liked our product and they wanted it for a core process of their business. They knew we were a small startup and they wanted to be sure we were doing things properly. So they asked us for a full audit of the code by a third party company. This external company was a big consultancy and auditing company and they run something like a 'due diligence' process on us and our code. Extremely professional and clear. They never had access to the full source code, only access to pieces they requested and 'only for their eyes' during a short period of time and always supervised by us. Since we wanted to close the deal, everybody worked hard to pass this test. Later on, we signed a source code escrow agreement.
Several years later, I was a working partner for a different company and same situation with a big Telco company. Since I had the experience I was involved in the deal, but this time this company did not want to play fair and it was clear that they wanted to copy the 'magic' of our solution. Their R&D division asked for the source code and they wanted it all the time they needed to study it by themselves. It was crystal clear from the early beginning they wanted to copy us, so we did not sign the deal. Then they tried to hire the core members of our development team for their R&D division.
So the lesson here is any company can screw you if they want and you don't protect yourself. You have to take risks when you are a small company, but your code and core team are sacred. I think most companies prefer to be nice guys rather than being a gang of bastards, but it's good to be cautious.
Find a good lawyer, or better get a good advisor on your board in your company to assess you on how to deal with this kind of negotiations. And never say 'no'; say 'yes, but we would like to do it under our conditions'.
Good luck!