Photo DNA cannot be as reliable as they boast
It's an educated guess, because I don't claim inside knowledge.
But I reach that conclusion on the basis that they're not making it freely available for home use. To be fair, it doesn't look like Microsoft have anything but honorable motives on this occasion (although I would question their own security - if the FBI comes calling are they in a position NOT to release such images?) (one of the many questions Facebook will also have to answer)
They make the software available in various cloud offerings and have donated it to a Missing Child charity amongst others. So why aren't they simply allowing us all to download a copy and do our own hashing and upload the results instead of the image - as suggested in the first post on this thread (John Robson)
I can think of only two possible explanations. First is that the process is so power hungry, you'd need a Bitcoin mining rig to run it. That doesn't look feasible from what I've read about the process. Looks like it might take about as long as creating a couple of thousand hashes. Under a second on most desktops.
The second is that they don't want it in our sticky little hands because it would relatively trivial to find ways to modify target images in such a way that they wouldn't be detected, so to preserve the value of the service, they don't want the great unwashed to access it.
In short, they're relying on "Security Through Obscurity" and, like most such attempts, that'll work for a few months, until the obscurity is cracked...
Oh, and by the way, the (partial )solution to sharing intimate private images is sharing one time keys which BOTH/ALL parties have to re-combine to access the images/data (as outlined in Digital Telepathy)