Yes, the dollar-for-dollar tax is the whole reason why it's plausible to think that Washington might dump their pick for salary relief. The question (hypothetical at this point) is how far we can go (under the CBA) to grant them relief and score the pick. I'm going under the assumption that the Wizards get the #2 pick because it sounds as if they'd hold on to Griffin if they nabbed him.
I believe simply taking the pick off of their hands for nothing won't cut it. It would save them $7.4M (the #2 pick is slated for $3.7M) but any number of teams could do that, so why us? If the Wizards are selling, one guess is that they'll be looking for as much relief as possible.
So the question is, how much relief can we provide? Well, let's go rosy and say we get the #1 pick. Take that and the #23, and at the start of July our total salary is at $50.2M, leaving us about $7M in cap space. The simplest trade would be to send Greene for Stevenson and the #2 pick. We stay under the cap, save them $12.2M this year and $7M next year, or about $19.2M over the next two years. We might have enough cap room to change out Songaila for Stevenson which would be worth almost $2M more to them, but we might not have the room.
In your scenario, the Wizards are willing to spend some future salary to get Martin, which is a reasonable assumption. I'm sure they'd prefer something structured like that deal rather than a simple dump for Greene, but I'm more hesitant than you are to deal Martin - especially if we can manage the same results without trading him.
Either way, it's possible to save them a good chunk of money. But how willing are they to give up their pick to do it? Is it a no-go outside of the Martin route? What's our front office willing to give up for (hypothetically) Rubio?