I think one of the issues here, Orobas, is that Fe tends to assume that when you accept help from someone, you are also accepting some obligations as well - expressing appreciation, using the circumstances to make improvements, being careful of their belongings, prioritizing needs vs wants, being in charge of those under your care (others don't feel comfortable reprimanding someone else's children), doing what you can with the resources you have so that you will be dependent forever, and if you are not able to do these, then accepting direction or help etc.
The woman cancelling her doctor appointments was harming her children, not the church people, and from their point of view it not only seemed irresponsible, but it also devalued the fact that they had reorganized their schedules to make it possible to offer a ride.
Some of these things really do seem obvious to us, even though I'm realizing that it is not necessarily obvious to others. This particular situation was one where the Fe users needed to set things up differently from the outset rather than making assumptions, so that both parties had a clear idea of what was expected.
Because Fe is action oriented, it tends to assume that information is conveyed for a reason and that if a problem shared has not been resolved, it is being shared because additional help from others is needed. Indirectly, the woman telling her story was taken as a request for help.
Secondly, for those that have not dealt with people who have not been raised in a healthy environment, it is hard to believe that these details are not obvious. For me, it's only been after repeated involvements with a variety of parents that I've realized that what seems quite obvious to me really is not, especially if your growing up environment normalized certain behaviours. For example, at one home I went to, the woman didn't find it obvious that condoms, alcohol, medicine, lighters and sex toys do not belong on floor level in the living room with four children under 8 in the house. It wasn't obvious to her that when you are cleaning a place, you move everything you can off the floor, put the garbage in the garbage cans (which means you need to buy garbage cans!), you put the laundry in the hamper, you put food in the kitchen and then you vacuum. It wasn't obvious to her that she and her children should bathe at least once a week. It wasn't obvious that it makes more sense to store foods that break apart and get dragged all over the house (pop tarts, raman noodles, ice cream cones, Hallowe'en candy, pudding) in the cupboard and that the cans stored in the cupboard would be better on the floor if there wasn't space for both. I felt almost as if I was being insulting by explaining that, as I helped her reclaim her house, but a lot of it was truly stuff she had not known or considered and she was grateful. It wasn't obvious to her that you can avoid a lot of problems by having a morning routine and putting the kids to bed at night. It wasn't obvious to her that it is dangerous for children to eat remains of food that have been left out on plates for the better part of a week. It wasn't obvious to her that you shouldn't give your kids constant access to treats if you want them to eat nutritious food as well. It wasn't obvious that covering the floor registers with a mattress will make the rooms cold. It wasn't obvious that not having a wallet and scattering important pieces of ID or money amongst garbage and clutter would have negative consequences for her. It wasn't obvious to her that you shouldn't leave your children with people who have a history of being sex offenders. This was a person who had access to some money and who had a beautiful house provided for her. She needed education and accountability though if those things were going to be of use to her or her kids. She had all of the extras and none of the basics.
The ISTP saw the woman agreeing to be a guest in a building that was not her home. The woman saw herself as being invited by people she didn't know to set up her home there. To avoid this confusion, it would have been better for the church to offer their help, but with guidelines in place which would have prevented resentment from building. They felt taken for granted and that the couple was not using this opportunity to improve their situation. They were concerned about the kids and so did want to help in some way. It would have been much better if they had presented a time frame and some expectations for what needed to happen to make the situation work. It sounds to me though that they had not foreseen what kinds of issues might come up.
I agree with you that it is not kind to offer criticism without helping a person to know how it could be avoided. They also need to be able to decide up front whether they are able to comply with what is being requested of them. To me this looks more than anything like a lack of experience in dealing with this kind of situation. Perhaps you can help them to see some of these things so that hurt or inconvenience on both sides could be avoided.