I don't think it says that at all. Because "accepting" is the right word here, as you point out. "Approval" is a different thing altogether. You can accept something without approving of it -- that's the main message in the Serenity Prayer and hundreds of self-help books that try to reframe that message, maybe to help it sink it, maybe just to grift a little.

If it was literally spelled out as "Your access is not conditioned on your approval" that could almost be taken as a threat -- you will access this whether you want to or not.

> For instance, your access of the website is not contingent on the website operator approving said access.

To me, this is clearly what it says. "(Your) access is not conditioned on (our) approval."

But, of course, since you read it differently, I have to agree that perhaps it's not as clear as I thought.

In any case, (a) it's not a request, and (b) if you truly want to control the narrative, then perhaps you should just do that from your own blog.