From what I've seen from Sky's offering (and this is mere speculation), I suspect the broadcasters send Sky their content as DPP compliant files, and Sky then re-encode and package the files for delivery to their receivers.
That isn't my understanding of the process. AIUI the broadcasters deliver a file in a format that the Sky boxes are happy with, and Sky don't have to do the encoding, just the distribution.
iPlayer and the other services have been on Sky for longer than DPP has been in use as well... (And DPP delivery is still far from universal)
I don't imagine they pull the existing files as used by the broadcasters services as their receivers require broadcast standard DVB/DTG complaint 'streams' (i.e. 1080i50 H.264 for HD). The broadcasters don't encode such files for their services as they usually deliver to progressive displays (e.g. computers, mobiles, etc) or newer standard smart TVs/receivers which are much more flexible in regards to the formats they support. The only service I know that does encode compatible streams is BBC iPlayer, which they use for some older smart TV's and the MHEG-IC service on Freeview HD receivers that don't support connected red button, however when I last looked at those streams the video quality was rather ropey, which I've not seen at all with Sky's service.
These days most broadcasters encode lots of different versions of their output for catch-up TV services - with different resolutions, frame rates, audio bitrates, video bitrates etc. as different encoder profiles. The source material will be 1080i - so encoding a 1080i H264 + AC3 5.1 file for Sky is just another (arguably slightly simpler) encoder profile, in addition to the others that are there to deliver for mobile, web, connected tv, consoles etc.
Delivering a Sky specific one would not be a tricky workflow - it just adds another profile requirement.
Certainly the quality of the video on the various catch-up services on Sky varied hugely at one point (not what you'd expect with a DPP delivery and a Sky encode). ITV Player at one point was sub-SD resolution whilst the BBC was high bitrate 1080i with 5.1 Dolby...