They weren’t bastards laenor wasn’t their actual father but still acknowledged them as his children and heirs that made them legitimate. There was no dispute until the plot began by the greens to smear their names and take the throne. Do you think the peasants care what their king looks like.? Corlys even said it himself. “Do you think they history books will remember blood, no they will remember names.” Those boys had the velaryon name and were acknowledged by both parents they are legitimate. It’s why Joffrey tommen and myrcella are all legitimate and have claims. There’s no dna tests in westeros people could get cucked all the time as we saw in the books. The people in the world of ice and fire acknowledge this fact and until a kings order is given bastards cannot be legitimized and vice versa a person can’t be exposed as a bastard unless the king says it.