It's true and it's a feature called UMA calling. The phone has to support UMA (software and hardware is involved), not just have WiFi. Several T-Mobile phones have this feature. It does work with most any router-- we test that service with a non-T-Mo router when we review their UMA phones and it works great. I believe T-Mo currently charges $10/month to use this service. Even if you don't use their router or Hotspot, you still have to pay the fee or they won't enable the feature on the phone.
No other US carrier offers this technology.