I agree.

Exactly. If we were really the card's target audience, as a bunch of unbanked cash users, we would be loading with stacks of $20s and $100s, so it would definitely be even amounts.

"hunnits"

People, the letter posted in OP references $1,000 and $500 amounts, not general even amounts. There are no data points on whether $800 or $876.36 is safer. Until we have such data points, let's not speculate.

Irrational float panic. The source of most shutdowns.

Blogs have their material for the next few days...

I don't think nice, round loads are the issue. If people (non-MS folks) load RB with cash at WM they will use round amounts $50 or $100.
I think odd numbers would raise more flags..

Not unless you brought your piggy bank with all those hunneds :p!

And here is that data point: the news of course hit the blogs and one commenter on View from the wing said:

I call BS. One person claims to have received this email, and the only corroboration comes from an FT account created today? Not convinced.

Think someone is trying to play a not-actually-that-funny joke here.

I'm not trying to 'play inside man'. I am simply able to comprehend the letter sent to the OP. It clearly states one of the reasons is $1K and $500 loads. The letter is very clear; no 'mystery' as to the two reasons why his account was flagged.

Inside man? No, I'm simply able to comprehend the written word. Which definitely states why they shut down the OP's account. Written at an 8th grade level.

... and yet that's one of the criteria written in the letter. Maybe you're right and AmEx/Target lied to the OP???

Why do folks unload immediately? Mind you I've not had the card for as long as many, but even when it came to other techniques, I always waited until the end of the month to unload anyway. Part of it was convenience - mortgage and car payment are due first of the month - but part of it just seemed to make sense. I figured Amex would probably want to have the float for just a little longer than 24 hours. I've tried to frontload the loading, and then billpay what I haven't spent toward the end of the month.

I do load 500/1000 at a time, but I don't immediately take it out. I've also avoided doing the 1000/500/1000 in a day technique, although I did once do back to back 1000 swipes. I also do some shopping at Target each time I go and use the card for that - not huge in the grand scheme, but it is, you know, a Target card and they might prefer you use it for its intended purpose every once in a while.

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.

If you draw a Venn diagram for even dollar amounts and loads of $1,000 and $500, one circle is inside of the other, but the outer circle is much larger than the inner circle.

You take the line out of context. The full reason is:

"Register "Cash" Reloads in $1000 or $500 increments
Withdrawals and/or bill pays equal to the account balance immediately following "Cash" Reloads"

The reason given is more accurately that poster was loading amounts of money and then withdrawing the same amounts quickly. Note the reason given in TommyFlysAlot's post:

"Withdrawals and/or bill pays equal to the account balance immediately following "Cash" Reloads "

Sure, it doesn't get much clearer if you ignore everything else and focus on only the one line.