Do you have anything to back those statements up or are you just pulling them out of the air?
Any PIP capability would be built into the chipset used for the DVR so the cost would probably be minimal, and the capability may even be in the chipset that DirecTV uses for their current DVR line. We know that the current chipset at least can do PIP with one program video stream and the GUI video stream.
The fact is that a second output decoder/processor is needed to create a second output. This is why Dish's 2-TV DVRs can do it, but their 1-TV DVRs, such as the dual-tuner HD-DVR ViP612 cannot. It's also why the HR2x-series cannot.
I grant you that it would probably only cost $5 in hardware costs per receiver (but don't forget software development costs), but DirecTV is looking at millions of receivers. $5 x 20 million HD-DVRs is a lot of money!
On a similar note, your statement of how widely PIP is used when available seems to be nothing but a wild guess.
I might have exaggerated the numbers, but as others already mentioned, there have been plenty of reports in the industry about how PiP never really caught on, and isn't much in demand overall. Very few people would list it as a "must-have" feature, though lots of people would be happy to have it if it was free. Not many would pay extra for it.
PiP is just one of a dozen features that DirecTV could have added to their DVRs. But designers have to look at production costs, and trim featuresets in order to stay within budget. That's pretty universally true in design work. Obviously DirecTV didn't feel that adding the hardware for PiP was worth the money, and given that the market hasn't run away from DirecTV as a result, it's hard to argue, even if you disagree personally.
DirecTV has to try to please a whole lot of people who all have very different ideas of what's important, but one thing that is very important to nearly all of them is the price, and the lower the better. In that environment, it isn't hard to see why an extra-cost item with a relatively low demand wasn't kept.
It's very telling that Dish didn't include PiP in the 612. Clearly they could have done so if they chose to, and they'd already paid for the development of the software and the design of the remote control, etc. But even with all that, they chose not to, to keep the price down. Kind of hard to dismiss that, don't you agree?