I've had one graduate student who completed a dissertation under my direction. So, yeah, if you know who I am you can find out who my student is, I know: I have nothing but good things to say about my student, and I don't think I'm going to say anything that violates Stu's privacy, and this has general implications.
My student will be in the UK this summer, and wants to visit some manuscripts. I am totally in favor of this, of course. Love the lovely manuscripts! And I'm happy to write a letter of recommendation to assert that Stu Dent did indeed complete a dissertation under my direction, blah blah knows how to behave in libraries blah blah please extend all courtesy to Stu etc etc. Stu has questions, of course, about how all this works. So I have gone with Stu to a local Rare Books Room (that is, not LRU's) to demonstrate how this sometimes works. I also try to provide guidance like "send an e-mail that says when you will be there and ask if you can have access to what you want to see, using shelfmarks."
"Ask" is a key word, and it's polite to use the library's method of referring to their holdings, rather than the nickname scholars may use. I have known snowflake-students for whom I might have found it expedient to dictate the e-mail, for fear of an overly-entitled demand to see restricted material, but this Stu is not one of them. (Come to think about it, if someone acted that entitled, I might not write in support. I'll have to think about that.)
But at a certain point, I say "Here's the URL for the website; poke around and find the address for the reading room you need, and the information about applying for cards." Or even, "I haven't been there myself, so do a web search for the library and see if you can find the information you need."
I think this is appropriate. Stu is now Dr. Stu, after all, and is perfectly capable of doing web searches. It's not that Stu expects me to do Stu's work; it's more that Stu is awed, excited, and nervous at the prospect of seeing Actual.Real.Six Hundred Year Old.Manuscripts!! (as one is), and wants to be sure nothing happens to ruin that prospect. So I want to be helpful and calming, but there is a limit to what I can or should do for Stu. Dr. Stu is going to have to go through the same process the rest of us go through.
I guess what worries me, a little, is that Stu thinks I'm someone special and important because I have been in these libraries and seen these materials, and I'm not. I mean, obviously I have a Ph.D. and certain training, but it's not as if my name means anything at all to Bruce Barker-Benfield. I have no "pull." I'm just one more obscure American scholar who has gone through the interviews with the gatekeepers to achieve a reader's card at various Significant Libraries.
In other words, to borrow from dear Miss Austen, I am a gentleman and Stu is a gentleman's daughter, and thus far we are equal. It's not as if my professors went with me anywhere but our own Ivy Library; they wrote letters of recommendation, but I don't recall any other specific advice about how to approach libraries and librarians.
On the other hand, their names and that of my alma mater opened more doors than my name and LRU's can do, and so, given that I do not personally have any particular clout, perhaps I do owe my students more individual help than my professors offered me.