Never say never, but the odds of winning an authentic Neil Armstrong or Apollo 11 signed item for way below market value in an auction format are exceedingly low. There are way too many collectors and dealers looking for Armstrong and Apollo 11 and trolling eBay 24/7. They are not going to miss an authentic Armstrong and let it go for way below market value.
If it is in auction format, and you got it on the cheap, chances are you didn’t outsmart everyone else. Chances are it sold on the cheap because it’s a fake.
You can get a deal on the rare occasion a seller significantly underprices an item and lists it as a Buy-It-Now. Then again… there are lots of trained eyes watching and you would have to hit it shortly after it’s listed.
If it’s a low-priced Buy-It-Now and it’s been sitting there for a while… yep… chances are it’s a fake.