IMHO, sometimes CSRs aren't fully accurate in what they say when they are talking to someone where they think something weird is going on. I know you know who you are and you opened the account and you're piggybacking as a side gig or whatever. But from their point of view you *could be* a spy or a scammer or whatever, and since they're not sure, sometimes CSRs take it on themselves to tell you something that isn't accurate, probably in a misguided attempt to put you off your *potential* scam somehow.
I think a similar thing happened to me when I added three AUs on my USAA card in three separate phone calls in under 24 hours. The CSR got suspicious and put me on hold for a while, then transferred me to a "specialist", who asked me some weird questions, and eventually relented and let me finish adding the AU.
In general I usually am honest and straightforward as much as I can be, and vague about the one thing I don't want them to know - that I'm getting paid to do this. Remember, there is nothing illegal about this activity, and again IMHO nothing immoral about it. It could be against their rules, and there is some risk there that has been discussed. But for me, if I ever get a card shut down, I'll be a little disappointed but respectful to the CC company, grateful for the money that I had made so far, and then decide on my next best move going forward given the new landscape.