The rule is one-inch thick soles. If you look at your own links, you will note that the TSA site specifically states "beach" flip-flops, sandals and thin-soled athletic shoes as less likely to be required to be screened by x-ray or explosives detection technology. This is consistent with the one-inch rule.

Here are my personal thoughts:

Some screeners misinterpet the rule to apply to the heels as opposed to the sole. If we were to apply it to the heels, then practially every shoe would meet that criteria. The rule applies to the sole, that is, the bottom surface of the shoe extending from heel to toe. This is consistent with the Richard Reid shoe bomb, and I have no problem sticking to that interpretation.

It is very difficult to determine the thickness of the sole of a shoe while standing at the WTMD. I try to be reasonable, and have attempted to train my screeners to be just as reasonable. The only tennis shoes I expect them to interpret as meeting the shoe criteria are the oversized ones with the huge padded soles. A great majority of tennis shoes do not meet this criteria as I interpret it, so as a general rule, I don't expect tennis shoes to be removed.

Screeners are only allowed to suggest, recommend or ask passengers if they mind removing their shoes. Passengers always have the option of keeping their shoes on. When a passenger passes through the WTMD and it alarms, the screener can view an indicator panel on his/her side of the WTMD which will light up in the general area causing the alarm. This allows the screener to explain to the passenger with a better degree of accuracy what caused the WTMD to alarm before offering the passenger a second attempt to clear the WTMD. Again, the exception is if the passenger is wearing shoes with thick soles, and those require additional screening even if they don't alarm the WTMD.

I don't believe in punishing passengers for not removing shoes that screeners may have misjudged as meeting the criteria for thick soles. I don't tolerate it from my screeners, and they are well aware of this. I don't tolerate intimidating or threatening passengers to remove their shoes. I do support explaining options to passengers:
I know that TSA is working hard to standardize this procedure across the board. I've read countless bulletins, updates, SOP noticies, memorandums and other pieces of communication trying to get TSA to remain consistent on the shoe policy. I can't explain why other airports have different interpretations of the same SOP. I think we have the correct and reasonable approach at our airport.