NDA's are normally written not only to prevent disclosure, but also to prevent the company receiving the information from using it to copy your product. If you're disclosing to a potential competitor, you don't want them sharing that information with anyone else, but you especially don't want them just stealing your codebase and using it themselves.
I went through this very same left-at-the-altar scenario a decade ago with a startup. It can be very difficult to prove that the company used the NDA information they had in their possession. Clearly the tech staff in the big company saw it, since this seems to be how they made the determination that they could do it in-house for less.
