> The energy stored in the oil is analogous to the "outside heat" for heat pumps.

This isn't correct. Here's a thought experiment to clarify:

If we burn X MJ of oil, we transfer X MJ of energy as heat to our house.

Otoh, if we set up a generator (say 40% efficient) which produces electricity from oil and dumps waste heat into our house, and use that to power a 300% efficient heat pump, we get 0.6X (generator waste heat) + 1.2X (300% * 0.4X) = 1.8X MJ of heat using the same X MJ of oil.

Thus,we get an additional 0.8X MJ of heat (80% extra heating) from the same X MJ of oil just by using a heat pump (& generator) compared to burning it. I.e we're using the energy stored inside the oil more efficiently.