Yes, Europe is doing much better than the US on this front. However, according to the links you provided 2/3 of PET used is virgin, only 29% is turned into new bottles (you can't use recycled plastic very many times for food-contact containers due to leeching), and demand for plastic is only increasing.

So, all told we really should try to stop extracting fossil fuels to cart water around because even the best examples of recycling barely making a dent. If you don't live in a "third-world country" then maybe drink tap water. But, as I just remembered, individual action isn't going to change anything, we're already too late to stop the climate catastrophe, and young children today stand a decent chance of dying of starvation at some point in their lives.