How do big companies of software developers check for bugs in their programs

I would say instead that each release of new features should be on a separate branch. This allows development and releases to be decoupled.

You are mixing two different concepts. One is verification, which is based on Unit Testing and Peer Reviews. This can be done by the developers themselves, without test data and its intent is to verify that a set of requirements are met.

The second one is validation, and this is done by QA (your testers). For this step you do need test data since the tester do not need to have any knowledge of the programming in the application, only its intended use cases. Its objective is to validate that the application behaves as intended in a production environment.

Both processes are important and necessary to deliver a quality product to the customer. You can't rely on unit tests alone. What you need to figure out is a reliable way to handle your test data to ensure its valid.

EDIT: OK, I get what you are asking. The answer is yes, because the Tester's job is not to generate the test data, just to test the application. You need to build your scripts in a way that allows easier maintenance and ensures valid data is inserted. Without the test data, tester will have nothing to test. Having said that, however, if you have access to the testing environment, I don't see why you can't you insert the test data manually rather than by using scripts.