The point of foil is to allow some air through. It's meant to keep out airborne contaminants (dust and such) carrying wild yeast and bacteria as well as insects like fruit flies that also could carry wild yeast and bacteria. I prefer to use foam stoppers instead of foil, for the same reason. As these folks said, the point of a starter is to grow a maximal amount of healthy yeast, not to produce a good tasting product. Where the point of the whole batch is obviously a good tasting product. As such, they have different requirements WRT oxygen.
In a starter you want as much gas exchange as possible without contamination. If you can use a clean room (some pros have them, most of us homebrewers do not) where airborne contaminants are not an issue, you'd get the best growth by doing your starters completely uncovered. And you definitely don't want your starter sitting undisturbed. If you're not doing your starters on a stir plate, you should at least be swirling them every time you walk by to keep introducing more oxygen.
But, once your yeast have performed their growth operations in the main batch, the only thing that oxygen is going to do is stale your beer. This is why you aerate before you pitch, and then do anything you can to reduce oxygen access from there on until the beer's in your glass.
The issue is that CO2 doesn't just sit there. Gasses will mix over time, and the blanket of CO2 would eventually mix with other atmospheric gasses. But it happens too slowly in a starter (you need oxygen more rapidly than that), and an airlock in the beer will prohibit it happening at all. If you do choose to ferment open, with using foil instead of an airlock most closely resembling open fermentation (a number of both pros and homebrewers do it, I haven't tried it personally but something I've been meaning to experiment with), it's common practice to then seal the fermentation with an airlock after the active phases when CO2 is no longer being produced at a rapid rate. You definitely don't want to just leave the foil on there the whole time.