Well, now you've been told by a former DirecTV employee that it doesn't.
Not all DVR's are even capable of being connected to your internet (non HD, for example, don't have a network port, at least the older ones like mine). I use it quite a bit, works fine.
I'm pretty sure that the iphone doesn't have an IR emitter either, the dongle either attaches to a cable box USB port or is an IR emitter on its own, that connects to the iphone via bluetooth (or wifi). Such a device would be at least theoretically possible with the Droid.
@captain amazing, the droid is capable of sending an RF signal, it's called "bluetooth". Bluetooth uses the same frequency range as an RF remote (2.4Ghz, just like WiFi, too). Whether you could convince the bluetooth transmitter to send the appropriate data is another question entirely.
The FIOS thing works because it can send data back and forth through the internet. So if direcTV, for example, decided to accept full remote commands via the internet, you could do the same thing easily enough, without any additional hardware.