I don't think this is true. I've never explored using Time Machine with a different router since I own a Time Capsule, but you should be able to use Time Machine with network attached storage on a non-apple router.
here's a tutorial for a Netgear router: https://kb.netgear.com/21360/How-to-setup-Time-Machine-with-your-NETGEAR-router
I don't think that is true for all Netgear products. I recently switched from extreme N base station hard lined to multiple extreme and express airport units. Was a very reliable system but not super fast. My dad bought me an Orbi mesh system with a total of three units, one base and two satellites. Speed is really nice compared to old airport system. Then I realized that Netgear/Orbi has yet to fully adopt adding external hard drive support to Orbi for network backups. TM backups have saved me a bit running cMP 2,1 on El Cap. Now, as a work around, having to keep external HD connected to one mac, and then share that network drive to other mac computers in the house for TM backups. It works, but definitely not plug-and-play.