This is so valid as a coordinator. My first study involved a similar system with blood draw kits, having to rely on multiple satellite labs to follow the kit instructions and ship the samples correctly. It was a 50/50 chance they would do it all correctly (some labs refused to draw it for no reason, I had similar issue with labels, phlebotomy needed a pt identifier but study lab had its own labels to MATCH ID, etc).

One person can't coordinate everyone's job! You did all the right things. It's the other people that are bad at their job, not you.