The case of
(let ((f #'(lambda ...)))
(eq f f))
has no bearing on the issue of whether (eq f #'eq) is valid. #'eq means
(function eq), which may or may not result in something being done at
run time to evaluate it; f is a variable reference whose value has already
"been evaluated" at some prior time. (eq f f) ought to always be true,
modulo some kinds of number-optimization.