From a 2008 article in Nature Photonics!:
To date it has been thought that APDs are unable to measure the number of photons in a pulse of radiation or a short time interval.And yet, from an article published four years earlier about APDs, we see:
A technique has been developed and tested that permits estimation of the photon number involved in a detection process.Wow. Just wow. I would have thought the reviewing process for Nature Photonics would be rigorous. I guess you can't believe everything you read.