I've heard everything about this from "something famous Greeks claimed to increase their prestige" to "a widely used and accepted euphemism for illegitimate children" on the topic.
Can you more clearly identify what you're talking about? Homer has a large number of divine epithets used of both heroes and gods, and not all of them are the same. Nor do all of them even refer to specific gods or treat the subject as a descendant of the god (e.g. διίφιλος, "Beloved of Zeus," an epithet used not only of heroes but also of heralds and gods). Without knowing what passage you're referring to it's quite hard to figure out what you mean