There is a clear misunderstanding among some between the two regulations.
Part 43 says what the maintenance/inspection record must contain, how it must be recorded and who can do it.
The "Sprit" of this regulation is to tell the mechanic (Or other qualified person) Hey! Do really good work, Dont Lie about it, Keep really good records by accurately describing what you did, Sign and date your records, in some cases provide the Total Time in Service. Oh, and by the way here are some other really important things (appendicies)....
Part 91 says who is responsible for keeping these records and which records required by part 43 must be retained & for how long.
The "Spirit" of this regulation is to tell the owner - Hey the guy qualified to do the work required by Part 43, just spent a bunch of time, effort (and your money) performing work (maintenance/inspections) on your aircraft, engine, or propeller. Some of those records are important to us(FAA)and to you. We only want to see these records if stuff goes bad, so make sure you keep these specific records. You, as an owner, will need the records when you sell the aircraft because the next owner will need these records and you are required to provide these records to the new owner. They dont have to take them, but you must provide them.