Dishwashers "Sanitize" at about 165 F. Some go higher, but most newer ones only sanitize to 165. (Do not know the time duration). That should be good enough. Also, if it has an NSF label on it, it has been certified to sanitize.
Two potential issues:
Over time the glass will fatigue and a "more than normal" number of bottles will crack on capping. (However, that should not be a significant increase... just think of how many glasses you have lost in the past year? One, two? and those go through many more cycles than your beer bottles)
The dishwasher is not a perfect cleaning instrument. Mine sometimes leaves some "gunk" in the bottles after washing. After heat sanitizing, it is likely sanitary gunk, but not attractive and may cause foam issues when pouring at a later date.
What I have been doing with success is keep a bucket of starsan available. Keep the bottles well rinsed after use, and wash them in PBW if your neighbor did not rinse them well. Then dunk the "clean" bottles in the Star San for two minutes, drain and fill. I have even put my Starsan in the Fridge to help the cooling process for the bottles. (Filling cold bottles from the tap is supposed to be better.. (Keep a lid on the container when in the fridge, however, or the humidity in the fridge will be too high and cause mold issues over time).
So, use the dishwasher if that makes sense, or jush change the liquid sanitizer method. I have tried both, and prefer the liquid method, but my reason was also encouraged because our dishwasher is NEVER empty!