Hi Jeff, I've been personally perplexed to see this one labelled as the Heuer AMI - without anywhere signed Heuer to be seen in the pictures!
Surely it has not the right dial, and considering it would the only Heuer-signed item to be detected from the pictures on the auction site, I find the official classification of this item as the AMI open to debate to say the least. We know that a number of other producers made this very same type of chrono's - Arctos, Sinn, Lemania themselves (though with slightly larger pushers). I'd say it would be natural to expect the Heuer one to have a Heuer-signed dial (although we all remember Rich's prototype). Furthermore, the eagle logo on the dial is similar to but surely not the AMI's official one - and the lack of the 3H sign also hints at a non-issued version - or at a replaced dial at least.
Definitely a picture of the inscribed caseback would have been welcome to allay some doubts- without it, your own comment that it is "nearly identical" to the AMI is a fair statement and all that can be said.
Cheers,
Fabrizio