This piece of info is actually news to me. Even if Hogwarts didn't have the bathrooms and equipment that it did later, I am sure that even when it was founded, it had something that all wizards and witches and muggles need - which includes bathroom facilities.
What was in the update regarding relieving themselves on the spot and vanishing the evidence would have been for some mischievous kids who didn't want to go some specific place or do some work when they had wands and magic. Of course, I agree that it would have made stuff miserable for the house elves.
Thinking further into the same - they could have used the room of requirement or like Dumbledore once said that he found a room only when he needed a bathroom. Maybe there are hidden bathrooms that were commonly used then. After creation of proper plumbing and bathrooms, people forgot about them. Since those rooms only appeared when required and no one required them anyone, there wasn't any issue.