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The library doesn't give access to a PDA. It gives access to stacks. The question specifically asks about the semantics of C, and calling functions to access an unbounded stack is just as semantically valid as using a pointer to access RAM. You might as well argue that C doesn't let you implement RAM, but only gain access to it. The distinction is meaningless.
Interesting corollary to the applicability of the linked-list loop detection algorithm: If a finite-state push-down automaton never repeats then it must use a logarithmic (in time) amount of memory. At the end of eternity it will have written to an infinite amount of memory.