While I am sure there is a point at which the string height (called "action") would be an issue for any guitar, it is probably way higher than most people would find comfortable. Therefore, you set it the way you like it. Whenever I have tested Epiphones and Gibsons in the store, they always seem to have really low action. Not sure if this is a factory thing, or the store.
There does seem to be a consensus that a higher action produces better tone, but a slower response (the string has farther to travel to get to the fretboard), and lower action produces a deader note but can be fretted quickly. Again, this is personal preference.
However, while what you describe can certainly be the case with a really low action, you might also have a bow in the neck. If the action was really low, you are probably all right, but if not, you might examine the fretboard yourself by sighting down the length of the neck. If it looks really curved, you probably should get a professional to look at it for possible tension adjustment. Some people do this themselves, but some people break the neck doing it themselves as well.