To treat the question in the original title ("True or false: If it cannot be tested experimentally then it is not science?") seriously I'm going to say "Sorta".
Assertions that are forever beyond experiment are not science. It wouldn't matter if they are built on the mathematical foundation of science. If there is no way they could, even in principle, be put to the test then you have theology or philosophy.
String theories1 aren't in that category.
Instead they are very, very hard to put to the test. Essentially impossible given the current state of experimental technology and of the theories themselves.
Feynman's objection was that the one easily testable prediction that comes from them--large extra dimensions--is manifestly false and requires a somewhat artificial patch--make them small and compact--to keep the theories in agreement with the world we know. That's not showstopper, but it is a little awkward.
There is a rough historical parallel in the state of atomic theory in the late nineteenth century. There were some pretty good reasons to believe that stuff came in discrete packages, but no really solid proof.2
That situation was largely resolved when a obscure German-born physicist name of Einstein thought up a way to magnify the otherwise unreachable small effects predicted by the theory to a level that the instruments of the time could observe.
Which points the way for string theorists to calm the agitated waters a bit: put some more time into figuring out experimental signatures that are accessible at foreseeable energies. And feel free to take "foreseeable" to include fairly blue-sky projects like muon colliders.
In the mean time the absolute, driving certainty that some well-known personalities exhibit to the mass media look a little odd for scientists.
1 And the multiplicity of them and the multiple free parameters in them matter: they make this a large family of theories with many different possible behaviors to try to sort out.
2 Come to think of it the luminiferous ether was another theory outside of experimental reach in the late nineteenth century that was put to the test in the early twentieth centruy. That one failed the test, which points out the importance of experiment in sorting these things out.