This is a good idea
First of all, if satellites aren't designed to be refueled then there is still a way to get fuel back into their tanks... through the rocket nozzle. Feed a flexible (and controllable) pipe in the back end and push it towards the fuel tank. Tricky but (I think... no, I'm not a rocket scientist) doable, surely.
It helps that the liquids involved aren't cryogenic things like liquid hydrogen or oxygen. Being hypergolic liquids will mean that TWO pipes are needed but still... doable.
The problem (of course) is the cost of getting a refueling satellite up there. If it costs the same as launching a new, upgraded-design satellite then there's not much point. Secondary payloads on SpaceX launchers?
But the continual love for the X-37 is really ridiculous. It (only, as far as I know) launches on an (expensive) Atlas V. And if you've get a satellite that can move around to meet other satellites, why add a layer of complexity by putting it inside an X-37? There's no value-added at all.