One difference is that today's page anchors are only put there by the page author, so, since all authors are cracker-jack security experts, they would not have made an anchor available in such a sensitive part of the document, since it opens their readers up to this risk.

As you can tell, I think that the difference is a real, technically true difference, but the implication is a bit dumb, since authors do not have this kind of thing in mind when deciding whether to anchor. You might as well be mad about lazy image loading too. If a browser is smart enough to only load images near an anchor, then this same risk would have been opened up when that was introduced. (The author wrote the anchor before lazy loading, so they correctly perceived no risk, then lazy loading turned it into a risk.)