It can be one or the other. The adults do remove deceased chicks (depending on size in my experience). I have heard anecdotally of dead chicks being fed to siblings but I've never seen anything like that ... and my question would be, if a chick dies, would an adult trust feeding it to its siblings. That and peregrines don't practice siblicide or infanticide so I'm not sure it's a normal response to cannibalize their own young - but I admit its just outside my area of knowledge/experience. As for outsiders removing chicks, I've done it before - both before and after we had the FalconCam. I can't think of any other times that a chick was missing from the nest without my having removed it from the box.
It is very sad to hear that the little chick didn't make it.
Just wanted to add a couple of things to TPC's reply. One year at Black Dog, one of the chicks did not survive. Mom waited for a long time, then very gently lifted the little one and flew out of the nest with the chick.
In 2008 at the Richmond nest, there was something wrong with the chicks and they did not survive. Mom again carried them very gently out of the nest.
And unfortunately, I have seen a parent feed a chick who did not survive to the other chicks. Several years ago at King, one of the chicks lived only a few days. Belinda waited and waited for Doug (her former mate, and Mae's last mate) to return, but eventually she fed the lost chick to the others. It was speculated that Doug had taken too long to come back with food for the chicks. It is not common to see this, but sadly it does happen.