Earlier quoted context omitted.
If you are notified in writing that you're banned from a coffee shop, but you walk up to the front door and the "server" (pun intended) greets you warmly and allows you to enter, is that "implied consent" that overrides the prior explicit anti-consent, and therefore undermines the legal authority of that ban?
I think almost any judge or jury would find it implausible if you told them you thought the written ban didn't apply anymore because the server still let you into the coffee shop. We intuitively understand that written notice from a property owner carriers more weight than the actions of one of their workers. I think the same exact reasoning applies where the "worker" is a computer server.
If someone was walked out of a supermarket and explicitly told that they were banned for life, and they tried to claim that the ban was lifted because the automatic doors opened for them, they'd be laughed out of court.
You could extend that further and say that the supermarket has a self-checkout. You may very well be able to walk through the automatic doors, grab something off the shelf, check it out yourself, and leave without anyone noticing you, but it's still trespassing if you've been banned from the store.