...nothing in Tolkien's writings that I can recall that *specifically* states "Gwaihir is the same eagle as the one in the Hobbit," although if they are not, Tolkien nowhere tells us WHY any eagle who happens to also be a lord of eagles should be indebted to Gandalf in LotR.  It's one of many little puzzles that we are left to think out as best we can with what information is available (and unfortunately, sometimes, that information can be contradictory or insufficient).

I've also learned to take certain things in Foster's Guide with a grain of salt, for two reasons: 1). there are blatant errors; for instance, he can't keep the name of Merry's wife straight, and 2). he admits that he draws only from the text of the novels, and does not incorporate information that has become common knowledge and was clearly stated by Tolkien himself in other writings, such as his letters and Unfinished Tales, even when those things are confirmed as fact by Tolkien's own son.  He will not, for example, say that the Istari are definitely Maiar, nor does he say that Gandalf is the Maia Olorin, yet to anyone who has read just the chapter on the Istari in UT, the evidence is plain.  And he also makes some statements that are rather puzzling, because the source of it is VERY unclear (such as the remark that the "seven stars" of Gondor are meant to represent banners emblazoned with a star that were flown by each of seven ships that came to Middle-earth from Numenor bearing a palantir.  If anyone can tell me where THAT came from, I'd be grateful, but thus far....)  The Guide can be a useful tool, but as with any tool, one must take care in using it.  :)

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