Well, considering most of the animals kept as pets are not naturally occuring wildlife, it is safe to say that they would not exist had we not been keeping pets. There are no wild packs of chihuahuas roaming the Mexican countryside, no great schools of goldfish migrating from lake to river, these are animals that only exist because humans were interested in a smaller version of a dog or fish that fit in better with our needs.
Also, freedom is a human concept that does not exist in nature. Social animals often do not have the "freedom" to breed, must wait to get their share of food based on the pecking order of the group, etc. Though my hamster has less spatial freedom than it would in the wild, it has fresh food and water, no predators to worry about, and the freedom to live a longer life that it would not have in the wild.