In a perfect world, what you suggest could happen. But we aren't in a perfect world! I belong to two guilds and bring our donated quilts to one of the charities we give to. I put them on the shelves, so I know they get there. I have also worked with kids who come in to shop - everything is free to them - and have helped them pick out quilts and pillow cases. I have also seen the pillow cases used at a free Christmas party for the kids. Each child is given a pillow case and then they go play some low tech, old school carnival type games, and win prizes. The prizes are then put into the pillow cases, and at the end of the party, the kids carry their loot home in the pillow cases.
Even so, I can't 100% tell you that all of the quilts are given to the children because I am not there 100% of the time. At some point in the process we have to trust those we work with.
That is the real problem with the RMH issue. The trust has been broken, or seems to have been broken.
One of the guilds used to give baby quilts to the local hospital, but found out that they were being sold in the gift shop for $10. That was less than it cost us (time and materials) to make the quilts, so we stopped giving them to the hospital. However, that might have been our fault - we may not have made it clear to the hospital who the quilts were for or what they were actually worth. Since I wasn't part of the process, I can't say more than that.