I hate to get bogged down in semantics but since we seem to be talking amicably now (yay!) I figure there's no harm in engaging a bit more. Feel free to ignore me if you don't want to continue our train of thought.
I would say Rescue fits into both of our definitions of DPS increases with different uses, though admittedly I think it's more in line with your view than mine.
If a dps has backed themselves into a corner where death is imminent and they are saved by Rescue I see that as the same situation as my previous PLD cover scenario - the dps would die without intervention but since it's on everyone in the party to best ensure everyone else's survival the Rescue is within the healer's base responsibility.
I don't think dps should expect it or rely on it (for a myriad of reasons, chief among them that Rescue is just not very responsive in my experience) in the same way I don't think dps should expect or rely on a PLD to Cover them in that same scenario or a healer to save them with a clutch Tetra or shield of some kind. The fact that it's nice that we have the ability to help mitigate the mistakes of others is nice but I don't see it as something to be relied upon. The goal should be to not put yourself in that situation in the first place. Anything anyone else does to save you once you make a mistake is a kindness.
The other issue I see with the Rescue as a dps increase accredited to the healer is that Rescue can actually be used as a real dps increase. It's rather common for healers to slot Rescue to yank PLDs back into melee range for the sake of uptime. While this dps increase may be hard to measure (with variance based on essentially how many GCDs are gained and then also what those GCDs are spent on) it is a gain that might be lost by using Rescue to save a dps who has made a mistake.
I guess ultimately I just think attributing Rescue as a dps increase is too complicated. The variables are too plentiful. Can it be an increase? Surely, but it doesn't exist in a vacuum like a flat buff or debuff does.