I very vaguely remembered something about this so I had to look it up. This t-mobile thing could have something to do with the Netflix Open Connect as documented on the Netflix site:
The Netflix Open Connect Initiative provides our millions of members the highest-quality viewing experience possible through efforts with Internet Service Providers (ISPs) to most efficiently deliver content. We partner with hundreds of ISPs to localize substantial amounts of traffic with Open Connect Appliance deployments and have an open peering policy at our interconnection locations.
Also I found this old gizmodo article.
It wouldn't surprise me if T-Mobile and netflix simply negotiated a deal to provide one of these appliances. And/or the special t-mobile edition of said appliance uses some kind of proprietary compression algorithm optimized for mobile bandwidth.
Obviously I'm only speculating but it would explain why this can't simply be applied to any/all video sites: the Netflix content is coming directly from a t-mobile data center as opposed to an unknown caching location or across the internet. Not sure why t-mobile can't simply say as much. Maybe they think it would make the net neutrality debate/complaints that much worse or maybe there's some kind of exclusivity deal and they can't discuss it?