Agreed. In my experience, being out of a job six months after starting a new one is a net negative. I can spin a longer break between jobs a lot better than that.
just leave it off your resume
Right, but then you're getting into the areas where talking about, say, a 12 month gap (4 months looking, 8 months working, then canned) instead of perhaps a 5 or a 6 month gap. It can be done, but it looks awkward, and it really sucks.
Or having taken on additional responsibilities (loan, started a family, etc) based on having the job.
Getting a job that shouldn't have existed and then losing it again isn't zero sum.