I’m sure there’s an agreement, somewhere, that grants them some sort of license to display your content — per your instructions — as a CYA. I’d take a look, if you haven’t. The section here that everyone (including me) objected to is largely boilerplate.
For example (and I know you’re not on Bluehost or an EIG shared hosting plan, but those are commoner than dirt):
Using your Content
You hereby grant to us an unlimited, non-exclusive, perpetual, irrevocable, worldwide, fully-paid, royalty-free, sub-licensable license to use, reproduce, modify, adapt, publish, sell, assign, translate, create derivative works from, distribute, and display any Content in whole or in part, along with the right to use your name and any other type of identifying information, including but not limited to any Social Media handle, profile picture, image, likeness, posts, statements or other information provided by you, in any form, media, or technology, whether currently known or hereafter developed in connection with the terms of this Agreement.
Pretty freakin’ broad terms, there. I wonder how many bloggers have ever bothered to read those?
Here’s the one for free WordPress.com accounts:
License. By submitting Content to Automattic for inclusion on your website, you grant Automattic a world-wide, royalty-free, and non-exclusive license to reproduce, modify, adapt, and publish the Content solely for the purpose of displaying, distributing, and promoting your website. This license also allows Automattic to make any publicly-posted Content available to third parties selected by Automattic (through Firehose, for example) so that these third parties can analyze and distribute (but not publicly display) the Content through their services. You also give other WordPress.com users permission to share your Content on other WordPress.com websites and add their own Content to it (aka to “reblog” your Content), so long as they use only a portion of your post and they give you credit as the original author by linking back to your website (the reblogging function on WordPress.com does this automatically!).
My web hosting company has a fairly odd variant — it needs clarification, in any case, but I have requested that, and questioned those derivative rights provisions found in it (not quite as broad as some of these), and received the following assurance in email:
“We aren’t interested in infringing upon anybody’s rights so I’ve forwarded this to the firm that manages our legal matters and asked if we can modify or remove it.”
We’ll see. But at least they responded. I’m not sure an EIG hosting company would.