I basically agree with your conclusion in practice as a thinking human being—but I'm also a writer, and it's very hard to write speculative fiction when there's no FTL and our nearest neighbor might live in the next galaxy over—so I like to ask the angels-on-a-pinhead questions anyway :)

So, a reasonable alternative solution: use the Anthropic argument. First, assume that there is intelligent life close to us. Then, realize that we still exist, and haven't been consumed by grey goo; and, according to our long-distance observations, all the planets around all the stars we've surveyed still exist too, in shapes that don't suggest intelligent redesign (even though "they" have had a few potential billion years to do so.)

Given that, it's likely that whatever path civilizations tend to follow eventually preclude them from wanting to leave to go redesign the galaxy in their image. This might just be a problem of limited extra utility derived from expansion: if Moore's exponential curve does, in fact, turn into Moore's S-curve, then there's no point in sticking more Computronium onto the pile, because the lightspeed-delay in the optical relays could just get to be too long for the extra circuits to do any good (presuming everyone wants to live on a single "instance" of AwesomeUniverse2000, rather than sharding it.)

Now, the number of additional assumptions in the conclusion can, by working back through Bayes' law, tell you how probable the assumption itself (that life exists close to us) is. I'm guessing it's a small, but not infinitesimal (compared to space) number.