Not estrogen as you usually think of it, but chemicals (phthalates in this case) that bind to estrogen receptors on cells and cause the cell to act as though estrogen levels were elevated in the body. The T in PET, which is what water bottles are made from, stands for Terephthalate.
I wouldn't trust the BPA free ones either, they probably have other pthalates or BPAB or something else - they can legally get away with advertising it as BPA free even if it has another xenoestrogenic compound that serves the same purpose.
Stick to glass and stainless steel.
I guess the real question is how much of this stuff leaks out when exposed to heat, and what's the equivalent dose in estrogen, and how long does it take for it to be excreted out. I vaguely recall that it stays in our system for a very long time and worse, they're in all sorts of things. :(
With a lot of the "leaking" stuff you should be concerned with it being exposed to heat, acid, and fat. That's why cans lined with BPA for things like tomatoes (acid) and coconut milk (fat) freak me out way more than water. That being said, I stick with stainless steel and glass for all bottles and food containers.