But maybe you have to see the two bullet points (loads and immediate withdrawals) together.
I would argue that high amounts for loading may be a red flag for them. Because it may hint that you intend to use the card not for its intended purposes. But I do not see why it would make the relationship sour for Amex if we load $500 instead of $493.71. What's the difference? You are not hiding anything from them. They see the whole transaction anyway.

At this point all of us will have to guess. But haven't shutdowns in other products in the past always been in conjunction with either 1) possible money laundering or 2) not being a profitable customer?
So, my guess still is that odd amounts will not save anyone. Profitable spending (at Target etc.) will.