That first argument just sounds like bullying and may be anti-competitive business practices. IANAL but I think refusing a specific person's access to your product specifically because they refused to sign a separate contract with you would be seen as a pretty clear case of you abusing your market control and probably some form of coercion. I'd love to see FB declare that - but it's much more likely they'd stick to "Oh, violated our TOS for some reason".
"Oh? What?... Oops, The Algorithm banned your fanpage because it was flagged, wait, let me check, ah yes, multiple reports of trademark violation on behalf of... Meta? Oh that's us. I apologize, it seems our employees were ever so vigilant but didn't know your app is a thing. An innocent false positive, nothing more."