I realize communication could have been better on both ends.
Sounds like the blind leading the blind.

However, glad to hear they were polite.
Now to provide constructive comments that you may want to think about before the free upgrade.
Although the 722 can only output 2 programs at once, 1 to TV1 and 1 to TV2, it can output 2 programs at once to many TV's. In other words, you can have TV1 Output going to the whole house on Channel 61 while at the same time TV2 Output going to the whole house on Channel 63. Of course any TV not located near the satellite receiver and connected using the appropriate cables will not get a HD picture, but will receive a standard definition (SD) picture, even on the HD channels/programming.
I suspect the installer ran/configured cables from the 722 satellite receiver to the other 2 televisions in the house with the 722 in dual mode; and if he setup the stereo agile modulator for both TV1 and TV2, everyone in the house can select whichever TV Output they wanted to watch by changing the channel on their local TV. Also, if you purchase a second 6.3 IR/UHF PRO remote with a Green Tab/Black 1/and UHF PRO etched on it, you can control TV1 from the 2nd or 3rd location, and leave the current TV1 IR remote in the same room as the 722. Such configuration would allow Bedroom 2 to watch TV2 and control it remotely, while Bedroom 3 watch TV1 and remotely control it. And hopefully, everyone in the living room went to bed.
You did not mention the model of the lower end receiver you are getting.
If its a ViP series, such as the 211, you will be able to receive on it, any HD programming you get on the 722.
But if it's a 311, standard definition receiver, it will not pick up the MPEG4 HD channels - not even as an SD output.
I believe all of the new ViP series only have a ATSC (digital) tuner, and will not pickup any NTSC (analog) signals. The stereo agile modulated output of the 722 is NTSC.
Depending on which Satellite Receiver you get, and/or what inputs your 3rd television has, hopefully you will be able to have the installer configure TV3 to receive the independent satellite signal from the new 2nd receiver, as well as the 722 TV1 and TV2 Outputs. Then you'll be able to watch precorded shows from teh 722, as well as HD programming (in SD mode).
And if your TV3 is an HD, or will be an HD in the near future, maybe you should call Dish and ask for a ViP 211 for that extra receiver.
One last thing...
Where do you want the new receiver?
As above, you should think about the future, will you be getting another HD set, will you be looking to get another HD receiver to go with it; and if so, maybe use that logic to have it installed in the other room the first go round (2nd go round). Maybe discuss it with the installer.