> Who gave the mail server permission to access the page?
The recipient of the email, or their employer's IT department that is paying another company for mail services.
If you send me an email with a link then I do believe I have the right to send that link to a third party service that can validate that it's not malicious. If I decide to sign up for a mail service that promises to protect me from phishing emails, then I [0] expect said service to read the emails I receive and examine the links within them. I would be upset if the service used the info I share with them for purposes other than keeping me safe, though.
I readily admit that I have, at various points in my life, signed up for services without reading the entire TOS that I agreed to. I try to choose companies that I feel I can trust to not abuse me too much, and sometimes I avoid certain services because I don't trust the company behind them enough to respect my privacy.
[0] I acknowledge that not everyone is as knowledgeable as me, and many people might not realize that this is how the protection works. So if the argument is more education, I'm in favor.