You're overthinking it. Well, it's in the name right? Its not safe for work. I'm in a semi-full conference room currently, and opening the link would be a bit awkward, as it would be really out of context for osmeone who have a view onto my screen.
It was definitely a valid remark, and in this case, it was useful at least for me.
I disagree that they're overthinking it, and you haven't addressed (or perhaps you overlooked?) their main point, that if this is true then you should have thought about that before opening _this_ link, instead of the links on this page.
This is more to say that this is a disagreement between you two at the object level, not someone overthinking a simple matter.
It was definitely a valid remark, and in this case, it was useful at least for me.