Although the pasteboard seems like a single thing, there are actually multiple pasteboards that run simultaneously.
When you drag something, the application will write a bunch of different versions of the thing you're dragging to the various pasteboards. Then, when you drag it to another application, that application will choose which pasteboard it likes best.
This is why you can drag an image to an image editor and get an image, but if you dragged the same image to a text editor, it would paste in the filename (or something).
One of the pasteboards is for URLs. Safari properly puts the URL of a dragged item onto the URL pasteboard, but Firefox apparently puts that information onto the String pasteboard, which Delicious Library doesn't check.
We have, experimentally, a kind of "media code super sniffer" that will work around this if and when we finish and merge it. In the meantime, someone should probably file a bug on Firefox (or just go in and fix it, Firefox being FOSS).