And they know what they're going to get if they go to a Baptist food pantry. If they weren't at least a little receptive to the idea, they would go elsewhere.
When I lived in Africa, I got to know some of the Baptist missionaries there. (I'm not Baptist myself.) They were incredibly hard-working, very dedicated to their work, and were all-around good people. The people in the church groups they supported absolutely adored them. Some had been living in Africa for close to 30 years; it was more "home" to them than the U.S. was, at that point.
And believe me, the last thing they were doing was driving around in new cars and such, as someone mentioned upstream. None of the missionary families were living in much luxury, at all.