You need to go to File > Import > Web Page… to see that (which will only be available if the selection is not in the Draft folder). I know you say you that this is exactly what you are doing, but I can’t see how the Finder open panel would open if so, as that would entail the code coming to life and deciding to do something different (and my programming skills are not that advanced… yet [evil laugh etc]). So, could you please indulge me and don’t take offence if I ask you to double check that you get this problem by going through the File menu and selecting Import > Web Page.
If the wrong panel definitely comes up even when you try again, try opening up ~/Applications/Utilities/Console.app and check to see if any errors get reported there about Scrivener when you got to open the Import Web Page sheet - code becoming intelligent jokes aside, the only other thing that could cause a program to do something it shouldn’t is a bug in which it throws an exception, and that would be reported on the Console.
When you drag links into the binder from your browser, by the way, be sure to drag the favicon (the icon next to the URL in the address field) - it may not work with all browsers, but definitely does with Safari.
Also, just to clarify:
Where did you drag the page from and to?
I’m not quite sure what you mean by this. Could you explain further?
Sorry you’re having problems - I’m sure we’ll figure it out with a little more information.