Here's the big issue, though - should ANY corporation be able to air commercials - because that's what those spots are - on public television? Remember - public television is supposed to be supported by citizens. If a corporation is making a tax-free "donation" to a program in return for a commercial, that's money out of your and my pocket.
Even though those spots are carefully crafted to ensure they don't contain a call to action, they are commercials. My son doesn't watch much TV outside of PBS, but he could spot a McDonald's and a Chuck E Cheese's from the car and ask to go there by the age of two. Obviously, as a parent, I'm in control of where he eats, but I'm not really happy with the idea that my kid is brand-conscious before he learns to read, especially when it's costing me tax revenue. If they want that stuff on Disney channel where it belongs, great.
About 10 years ago, anybody could use "corporate sponsorship" as a tax-free way to get their brand on anything, particularly college football games, which had TV audiences that gave corporations a huge bang for their buck. When the government figured this out, they set up stringent rules about what counted as a "donation" and what didn't. This really hit the arts hard, and right around that time the NEA was shut down. Corporate sponsorship became the only way for arts organizations, PBS among others, to survive, and they worked out those cute little "greeting card" spots where any product can "thank" PBS and wave its brand in your face. Note that none of the foundations (who have nothing to gain) have anything but a mention and possibly a logo.
I don't know about the connection between kid's TV and obesity, but don't kid yourself that this issue doesn't matter. It's costing you millions of dollars in taxes. If we want public television to be truly public, then we have to find another way to finance it.