You didn't need additional confirmation because it was the only information provided with no revelation later on that it had been incorrect. Other deceptions and misconceptions had been reversed or revealed at some subsequent point as needed--including Snape's true loyalty. Therefore Rowling intended the information provided by Lupin and Sirius to be reliable. It was only the preferred dislike of those characters by Snape fans the deemed their information about James and Lily to be unreliable. Again, a perceptive problem caused by a personal biases.