MTTF (Mean Time To Failure) is irrelevant in theis case... a .22 rimfire round will add the same cumulative fatigue damage regardless of the time span.... cycles to failure is the only concern. For a minor, repairable/replaceable part, a low number of cycles to failure may be acceptible.
I'm not sure where you got the figures for the M9, but they sound awfully low. I'm not certain of the requirements that it had to meet, but in Vietnam, we had pre-WWII 1911s that had to have seen 100,000 rounds or more... they saw service in WWII, Korea, and Vietnam, as well as having been issued for training stateside in the interim. I recently sold a Ruger Red Label shotgun that had over 75,000 rounds through it, and bought an SKB 85 TSS, as it is a more serious competition gun. A shooting buddy has an 85 TSS with over 100,000 rounds through it, with no failures yet.
And, yes, cycles to failure is a statistical figure. In the engineering profession, unless otherwise stated, it is generally assumed to be a B-10 life... in other words, out of a large sample, 10% would be expected to have failed by the given number of cycles, while 90% would live past this point. In an extremely critical application, a B-2 life or even a B-1 life may be specified. As a side note, for ferrous materials, fatigue failure is generally a log-normal distribution... if I had my notes handy, I could give you the Weibull slope of a typical fatigue failure distribution for ferrous materials.
MTBF is, in this case, irrelevant. It applies only to recurring failures in a repairable system, and is generally associated with MTTR (Mean Time To Repair). MTBF and MTTR are used to calculate probability of mission success within a given time window.
If you feel like learning a whole bunch about metal fatigue (both ferrous and non-ferrous), get a copy of SAE standard J-1099. I was on the committee that originally wrote 1099 back in 1975... and, until I retired, I was an ASQC (American Society for Quality Control) CRE (Certified Reliability Engineer), so I'm not just blowing smoke up your skirt.