Why does a university not require me to send proof of high school degree? I'm applying to a online Bachelor of arts degree at a very well established university in the United States.

However, I'm almost through the application process and at no point did they require an actual print of my high school diploma. They simply asked me to sign (digitally through docusign.net) that I have completed high school. I've been corresponding with an agent of theirs and according to him they are just reviewing what I've sent them (which does not include a diploma) and after that I can enroll. 

I do have a high school diploma but how come they don't require proof of this?

EDIT: Continued story:

I recently got accepted into a university and they had me attest to having a high school diploma, which I did. After being accepted without needing to provide any proof of having said diploma, I naturally asked why they didn't ask me to provide proof of graduation.

They replied: "We randomly select 1 out of every 20 students to provide further documentation. You would’ve been selected at this point so it looks like you were not chosen."

Is this normal in the United States? Where I'm from (Iceland) this just sounds plain weird...That potentially 95% of students can get in without a diploma at all?
This is not normal in the US -- but that doesn't mean it's an illegitimate process. Private institutions can select applications using whatever criteria they deem appropriate; so while it sounds a bit questionable to me, it's perfectly within reason.

It is also perfectly valid to admit students without a high school degree; it happens to be uncommon, but depending on the subject matter of the BA, it may not be (at least in the university's eyes) a strict necessity, provided your other credentials are sound.