Ok, once that has been experimented with, I see it. But it's not that simple.
First, photobucket labels it a Direct Link, a definite label. Your lack of capitalization says you're giving me a general term, not quoting the name of the thing as it appears on the website.
Second, when I first uploaded the photo, I could see the photo on the site but the box with links had not yet appeared.
So, after that box shows up:
Third, the "Links to share this photo" have four entries:
Email & IM: okay, it's probably not that one
Direct: what is there, without one of you telling me, about the word "direct" that implies that this is the one to choose?
HTML: what is there, without one of you telling me, about "HTML" that tells me to use this or not to use it? After all, you can enter HTML on this site.
IMG: In earlier years, you'd use imgspacesrc, just as Daniel explained in one of the posts in this thread. Sometimes you still have to use it, as Daniel explained. So what about this title all by itself says I should not choose it?

By the way, after I clicked on "Direct," the label "Email & IM" changed to "Direct" ! !