Can a simple program be responsible for a BSOD?

Just because your program isn't a driver doesn't mean it won't use a driver.

In theory, your code shouldn't be able to BSOD the computer. It's up to the OS to make sure that doesn't happen. By definition, that means there's a problem somewhere either in hardware or in code other than your program. That doesn't preclude there being a bug in your code as well though.

The easiest way to cause a BSOD with a user-space program is (afaik) to kill the Windows subsystem process (csrss.exe). This doesn't need faulty hardware nor a bug in the kernel or a driver, it only needs administrator privileges¹.

What is your code exactly doing? The error message ("A process or thread crucial to system operation has unexpectedly exited or been terminate.") sounds like one of the essential system processes terminated. Maybe you are killing a process and unintentionally got the wrong process?

If somehow possible you could try to get a memory dump from that customer. Using the Debugging Tools for Windows you can then further analyze that dump as described here.

¹Windows doesn't prevent you from doing so because it "keeps administrators in control of their computer". So this is by design and not a bug. Read Raymond's articles and you will see why.

Short answer is yes. Long answer depends on what is you program is suppose to do and how it does it?