The users click the button, get told it worked, but their comment is not visible to them. The fact they can't see it is why they suspect a problem I think.
A UX improvement might be to update the success page to show their message back to them with a prominent "Pending review" message very close and very obvious next to their message.
e.g. on hackernews comments are submitted fairly quickly, and I find myself reloading very often to check if the comment really has been placed.