Maybe your SIL was trying to let you know that in their family, it is customary for children to offer accommodations to their visiting parents.
It certainly is in mine. Considering that they are my actual parents (or my DH's), and they put themselves out on my behalf so often during my childhood, I make sure they know they are welcome and invited to stay.
If my kids were grown and I went to visit their town, I honestly would be hurt if they didn't offer for me to stay at their place (unless their place was so tiny; and then I would expect them to say, "Mom, I'm sorry I can't put you up, I just don't have room).
If they had romantic plans for the next morning, I'd expect my kids to say, "I'd offer for you to stay, but it's Sweetie's birthday the next morning, and I was planning some quiet time."
So, I don't think you were rude at all, but you and DH should probably discuss what his family's patterns are, and how you're going to respond.