Hi, Jeff. If your parents aren't going to be using any of the internet options (such as Netflix streaming or BD-Live), then having an internet connection isn't important. Just make sure that the blu-ray player allows firmware updates via disc (I have yet to see one that doesn't), and you're all set.
My Panasonic DMP-BD60 has an ethernet jack on the back, but I almost never have it connected to the internet. I've updated the firmware both via the internet and via disc (that I burned on my computer from the internet site), and both worked just fine.