I think it happens only if you have a broken device driver, applications cannot cause BSOD with memory allocation.

Does it BSOD if it runs out of swap space though?

Well I beg to differ, using a unlimited swap file can quickly reach hard issues after 64gb of swap use. At that point mallocs in the windows ui fail (timouts or something?), that apparently are not meant to, eg fonts from shutdown menu missing, the system being unable to shutdown ect.