frontlefthamster,
Is there any evidence that runway overruns are more common in private operations than transport? I don't think so...
I think if you visit the NTSB website and research Citation accidents, you'll find that the majority are caused by landing-related problems, such as over-runs.
I haven't made an exhaustive study, but the impression one gets is that most of these accidents occurred during private operations. My reasons? Most of the smaller Citations are certified for single-pilot ops and many are flown by owner-pilots. Nothing wrong with that, except for the self-induced pressure to plan a flight to a runway that just meets the book figures for landing distance, making a mess of the landing (height, speed, touchdown point, retardation, etc) and then not salvaging the situation by going around.
I agree that 1.67/1.92 can seem excessive at times, but experience has shown that even professional pilots get it wrong sometimes, and that extra distance may just save the day.
I advise my private Citation pilot friends to plan their landings with a factor of 1.5. This seems sensible without being unnecessarily restrictive. The Cessna AFM factors the dry distance by 1.35 for a wet runway*. Using 1.5 as a planning factor means that even if you arrive and find that the runway is wet, you'll still have an 11% margin over the AFM wet figure. (1.35 x 111% = 1.5)
If you insist on private operators using public transport factors, you'll lose credibility. They will say, 'I saw Joe land on that 3000ft runway with his CJ, so why can't I?' Better to give them something realistic and to educate them in the critical importance of flying an accurate approach, using the correct stopping techniques and most of all emphasising the need to go around if in doubt.
The other day I watched from the RHS as a private CJ owner/pilot landed on a 'short runway' of 3650ft. He stopped in 2600ft. The AFM predicted 2650ft. The public transport required distance would have been 4425ft, which would have made our landing impossible. It would have been very difficult to convince him that what he just did was 'dangerous'.
This was in daylight with a dry runway and a slight headwind. Also, he placed it on the ground at the right speed, in the right place and did a great job of selecting ground flaps and braking immediately. That's why he made the 'book' figures.
In other words, this was a 'best-case scenario'. The safety factor under these conditions was 3650/2600=1.4 which is not bad, but still less than the recommended 1.5 for private flying and considerably less than the 1.67 for public transport.
The safety factors may seem excessive, but they are there because it is so easy to get something wrong (speed, height at the threshold, touchdown point, delay in selecting ground flaps, etc). He got it all right!
But to get back to the original question: I think it's already been answered.
For planning, you must apply the factors. Once you are airborne, you should still check that you meet the factored performance when you arrive at your planned destination or alternate (and you should, barring unexpected tailwinds en-route). However, if you suffer an in-flight problem that increases your LDR, or if you divert to an unplanned diversion airfield because of an operational issue, my understanding is that the AFM figures can be used at the PIC's discretion. This 'alleviation' should of course not be used to take advantage of any defect that factors the LDR by less than the public transport figure!
*US registered CJ series. Figures approximate.