I just tried this today on a dummy account, and it worked just fine.
When you're at the mission start screen you will have the opportunity to send your passengers on scavenging missions. In this section you can heal them if they're not 100% on condition, equip them with their prefered weapons, and determine what they're going hunting for. If they have been damaged and you have a MRE you can use it on them at this time to work towards this trophy. A very easy way to cheese this trophy without having to loose 25 of them (you need to use 50 on yourself for another trophy) is to fill the survivors to max health. Start the mission and immediately pause & select restart mission. You can continue to feed them and restart until you have your trophy completed.