I think you may be reading into this a little bit too much. If you gave instruction, you log "dual given". It doesn't matter how the student logs it. The student has total control over his logbook. If that were the case, then an ill-thinking student could erase the signature from his or her logbook and get the instructor in trouble.
An erasure would leave evidence of the original signature. In any event, the regulation is binding on the instructor -- if s/he gives instruction, the instructor
must sign the trainee's log -- no ifs, ands, or buts.
And secondly, a pilots logbook means diddly squat to the FAA. The FAA can't violate you over just having something in your logbook.
Actually, the FAA can and has violated instructors for what they wrote or didn't write in their trainee's logs -- several times such cases went all the way to the full NTSB, and were sustained.
The crime is when you try to pass off falsified times on a 8710, or some other "official" FAA document.
While that is a violation of 61.59, there are other regs you can violate with false entries without filling in another "official" FAA document, starting with 61.57.
A lot of people mistakenly assume that a pilot's logbook is a legal document that the FAA can look through at any time and violate you over.
It's no mistake. They can, and they have. There's plenty of case law to support that. They even once violated a pilot for a flight made some 10 years back listed with a passenger because there weren't three takeoffs and landings in the preceding 90 days -- and that was sustained all the way to the NTSB. This logbook inspection came when the pilot presented the log to the FAA to show he had enough aeronautical experience to take the ATP written test (back then, you had to have the flight time to take the written, not just the practical, and you presented your logbook, not an 8710-1, to do that).
"Hi this is the FAA, let me see your logbook... Oh look this flight you just completed 20 minutes ago was logged incorrectly, you are hereby VIOLATED!!" I don't think so...
Think again. Imagine they look at your log on a clear blue day (say, on a ramp check, when they see your log in plain sight in the airplane), and you have logged an instrument approach to that airport without a safety pilot aboard. You won't like what happens next.
BTW, the FAA can demand to see your logbook anytime they feel like it, without cause or reason, and the only thing you have is a "reasonable" amount of time to go get it and show up at the FSDO. 14 CFR 61.51(i). If they find any violations of the regs during such review, you're on the hook, and they can use your logbook as documentary evidence in the proceeding.
BTW, for a case directly on the original point, see
Administrator v. Luyten. Mr. Luyten lost his CFI ticket for 60 days for failing to sign a trainee's log.