Oh, they swim. As ten year old kids, a friend and I hiked about a mile into some woods alongside a river in SE Oklahoma (Skunk ape territory), our second camp out without supervision. We set up camp with some lightweight cots and little else. In the middle of a sleepless moonless night, we heard something drop into the river just upstream and across the river from us. We heard loud splashing as the ‘thing’ slowly made it across the river. We couldn’t see a thing as the fire had died down, but within a minute or two I heard my buddy screaming like a little girl. Something was under his cot and bucking wildly trying to get out from under. I found a flashlight and was able to see that the ‘thing’ was a very wet armadillo. So, yes, I happen to know that an armadillo CAN swim.
Of course, being a well-mannered future Freeper, you never mentioned this to him again, did you :-)