The FAA takes falsification pretty seriously. If you are willing to falsify one document, what is stopping you from doing to others? Aviation is largely built on the honor system, and if you break that honor you can't be trusted. One false entry in a logbook makes that entire logbook suspect. After all, how can they trust anything you wrote in there.
Once upon a time when I was in college, one of my fellow students thought he had a smart way to "build" time. He figured if he padded his logbook with school aircraft, it would be too easy to trace. While in school he worked the line for the FBO, so he decided to use random tail numbers of transient aircraft he would fuel while working, thinking it would be harder to track.
At his next checkride, the DPE noticed something familiar in his logbook. He started asking him ,"Oh you've flown N12345? Was it a good plane?" Dummy didn't realize the trap that was being set, and played it off, "Oh yes, it was a real nice plane."
Then the DPE dropped the bomb, "Interesting, you see I've owned N12345 for the last 20 years, and I don't recall ever letting you fly it." Our ambitious student had inadvertently picked the DPE's personal plane to pad his logbook. DPE kept his logbook, turned it into the FAA, and said student transferred out of the aviation program.