I think avoiding what you call "debugger-induced tunnel vision" can be done by using a debugger to step through the code just to read it, debuggers can also be tools to better understand what the code is really doing because you not only see the code but also the state the system is in while debugging.

The added benefit is that when you actually break out the debugger to squash a bug you better understand what might be going wrong as you can try and pattern match from the time it worked perfectly.

I treat the debugger as a tool for understanding code, buggy or otherwise, no "debugger-induced tunnel vision" for me, it widens my field of view :)