Factsheet
Under the normal circumstances that your question present (i.e. dynamic linking to a library assumed to exist on the user's system and thus not distributed with the program) the following part of the license text will save the day for any program using glibc:
A program that contains no derivative of any portion of the Library, but is designed to work with the Library by being compiled or linked with it, is called a “work that uses the Library”. Such a work, in isolation, is not a derivative work of the Library, and therefore falls outside the scope of this License.
Whatever the glibc license is, it implements, as you note, standard C lib functions. That is, it implements a standard API. Consequently, a program which uses functions from the library (without modifying the library) cannot be considered a derivative work of the library (because you could replace the library by any other implementation of the same standard API).
That being said, if you bundled the library along with your program and distributed the whole, you would still be bound by some of the terms of the license, but if you just assume the user's system has a standard C lib and dynamic link to it (as suggested by @MansGunnarsson), then you are not bound by any of these terms (whatever they may be). So the question of the license being LGPL, GPL or proprietary does not matter anymore.