I asked the initial question because, as a linguist (with a job in a cognitive science department), I was a little puzzled about the singling out of linguistics as a field that is insular or outdated or in any way about to expire. In fact I'd say it is rather thriving, though it may be that the balance of research across subfields of linguistics is not what it was in the 70s (i.e. Chomskyan syntax is not at its apex). Modern linguistics is and always has been a tiny field, so this may make it seem isolated in some way. (Like, there are subfields of psychology that seem to be about an order of magnitude bigger than all of linguistics.) There are few large linguistics departments, and many schools lack one altogether. But abuflletcher's initial comment as well as a lot of the followup comments have lacked any specifics that I can easily identify and address, so I guess you'll just have to take my word for it that the field seems to be in decent shape and isn't about to die. (And has by no means run its course.)
My impression, and feel free to correct me, is that linguistics needs those fields much more so than those fields need linguistics. I know to some degree it is just cross disciplinary hackling but in my experience with folks in those fields they are pretty skeptical about the linguists perspective. I can't say anything about linguistics on intellectual grounds, but it seems to me that the profession is not in a good place.
I don't know that there is particularly extensive need in either direction, except in two ways: collaborative work between linguists and psychologists has been extremely fruitful on both sides, and will likely continue to be, and linguistics has lately been adopting many experimental methods from psychology (and to some extent cognitive neuroscience). So we do need psychology etc because the methods are well-developed, and as a much much larger field, there are many more people actively working on methodological issues. But I don't really see how this need puts linguistics in a particularly bad place. I actually don't think that the skepticism is much more than cross-disciplinary heckling compounded by the fact that linguistic theory is much more complicated/developed than theories of the mind in other domains, so it is easier to go into a linguistics talk and not understand it, than to do so for a psych talk (which will be about a series of experiments, not a theory).