DSL? It has nothing to do with DSL.
The receiver overlays the caller id over top of the program it has recorded but it still has to send it out to the TV through what ever type of cable your receiver is connected to the TV with so you can see it on the screen, the DVD recorder records everything that is fed to it through the connection to the receiver.
The caller ID pop up becomes part of the signal being sent to the DVD recorder, but it is not recorded on the Dish receiver
The DVD recorder or VCR or stand alone Tivo or what ever the recording device is, records whatever is being fed to it & the TV. If you hit the info button while recording guess what, the info window gets recorded on the DVD but not on the dish DVR recording, if you hit the guide button the guide it is going to show up on the DVD recording but not on the DVR recording, hit pause on your receiver & the pause bar will be recorded on the DVD.
All those things are overlayed over the DVR recording, but become part of the feed when sent to the TV or DVD recorder or VCR or whatever.
The DVD recorder does not know that the caller ID pop up should not be recorded & even if it did has no way to separate it from the show underneath of the pop up