The site guidelines also say to assume good faith, to converse curiously, edit out swipes, not go fulminate, and to avoid grandstanding.
Before calling me dishonest, did you stop to consider that maybe you didn't understand my comment, or that you weren't clear with your meaning?
I genuinely don't think you understood what I wrote.
If I operate a business, you are not necessarily entitled to transact with me how you please. I can implement whatever rules I want so long as I am not outright committing discrimination against a legally protected category and so long as I am upholding other fiduciary obligations.
For all you know, the site operator is opposed to AI agents on moral grounds, or has beef with the developer of the specific LLM interface you are using.
More practically, an e-commerce website often won't make a profit if a purchase is too small. If they find that LLM users are easily bypassing their upselling tactics that usually result in higher basket sizes, then ideally they would adapt their approach to LLMs or implement a minimum order size, but they are also perfectly within their rights to simply ban you.
I am not saying that this is the likely reason -- just that there are reasons, many, and often they aren't very obvious unless you are in their shoes.
Every kind of business does this sort of thing! A software consultant or designer might only take money from healthcare companies, and not talk to anyone offering (apparently, to a naive outsider) equivalent work in a different industry. A restaurant might implement a dress code. A cab driver might insist you not wear strong perfume.
Some rules that externally seem flippant and unreasonable exist for reasons that are entirely sensible, but also entirely nonobvious externally. In any event, I don't agree that your usage is equivalent to a manual session, if it were, the operator wouldn't be able to detect it! Therefore they are within their rights to detect this and disallow it. There are plenty of reasons that they might do this, and unfortunately you probably don't have the information needed to interrogate those in a meaningful way