Just for fun, you should do a Google or other search with that question and see the answers that come up. They all sound plausible until they don't. I'll save you the trouble, but some of the answers have to do with the possibility of stagnant and or contaminated water back flowing into the mains, others seem to say without a back flow, their unit turns on randomly when cold water is turned on the home and a host of other ideas. For every idea suggested there's a pro dismissing it for one reason or another. Even the dismissals need to be dismissed; one pro says you don't need back flow since "the city water meter has one built in". Sure it does...but that doesn't explain why I have to have a costly dual RPZ on my irrigation system, and have it tested yearly!
The most plausible in my opinion, is the one that was actually related to pumps, not tankless, when it said "to prevent back flow so the pump doesn't lose its priming". Now, I can get behind that one! In my former weekend home in Michigan, (well and septic), the water system (hot AND cold) in the home would "lose its prime"; meaning, the water in the homes pipes would drain, air was introduced and when you arrived on a Friday night and started to use water, every fixture would spit, burp and gurgle until you finally got all the air out of the system. Had I put in a check valve or check valves, this likely may not have happened.
As for the Rinnai vs Navien vs Noritz or whatever...some regions of the USA and within states and communities have better representation than others. Here in the Charlotte NC area, Rinnai is the one installed almost exclusively. Navien has only one rep in the area and they are not that close...so trained techs and service and parts are harder to find. If you are a plumber in this area and you install tankless, you are going to spec Rinnai.
Years ago when I needed a tankless for a closed loop driveway heat system, the ONLY manufacturer who certified their tankless for closed loop circulation systems was Takagi. So that's the one I got.