The sales reps at both DirecTV and DISH lie. It's well known. Lesson learned: don't trust a sales guy. EVER. FOR ANY REASON.
I have friends that have DISH, and I have DirecTV. There's no way I'd ever go to DISH -- I absolutely hate their receiver interface, and the way their receivers hook up to the TVs (two TVs to a single receiver) makes me want to murder an engineer.
With DirecTV:
If you're wanting to use their whole-home product, yes, you need the DECA adapter. While the receivers do have RJ45 jacks for network connection, they are designed to be used strictly for internet connectivity, not for streaming video. Some folks have gotten it to work that way, without any problem - and some haven't. DirecTV's position is that if you can get it to work, fine, they'll activate whole-home DVR services on your account, but they'll set an unsupported flag on your account. If you want them to support your whole-home service, you need to have them install the DECA adapters.
Someone mentioned an AM21 -- that is for receiving over-the-air programming (from a broadcast antenna). The vast majority of DirecTV customers don't need it, as local channels are rebroadcast on satellite channels. If you do need an AM21, that's an extra charge for the device (though DirecTV will frequently reduce its price or provide credits to make it free), and you're responsible for the antenna and cabling from the antenna to the AM21.
With the whole-home service, you can have two active HD tuners per HD DVR operating at any time - be it recording something or watching something. On top of that, you can be watching something on the TV connected to that DVR, and additionally streaming something from it to another HD DVR or HD Receiver elsewhere on the DECA network. Each set top box connects to only one TV, but a DVR can provide service to multiple TVs (and that is what they are marketing) because you can access that DVR's functionality from any HD Receiver on the DECA network.
As far as remotely scheduling records, they do have apps, and you can also schedule recordings from the DirecTV website, without any app.
Why do people believe sales agents?

:cry;
<edit>
Re-reviewing the thread, and have additional comments:
Also, why do you need an RF remote? IR will work for most people.
For what it's worth - the whole-home DVR service works with any of their recent HD DVRs -- you do not need the latest and greatest DVR to make it work. The main advantage of the latest DVR is just speed - there's no functionality change between them.