To go back to the initial question the answer is "yes." If you see something on Thingiverse and you find that it has no Patent Pending or Patent, you can in fact get it patented. What the Patent Trolls are doing is intimidating people. It's a real problem. They are well funded so most people are not going to be able to outlast them in court so will just give up on their dream. These unscrupulous people are really killing the American Dream of entrepreneurship and product development. There are a few Senators who have recognized this problem and from what I understand are working on Bills that might help slow the Trolls down.

In product development there is a document called a Non-Disclosure that you get everyone you share your design with to sign. That prevents them from running off the second you leave and securing a patent on your idea. Thingiverse does not offer you any protection. If you show it someone can steal it and with enough lawyers, can falsely prove in court that they had it first and that you saw it from them. You won't win the battle. My advice would be that if you have a really good idea, never post it on Thingiverse or anywhere else until you at least get a Patent Pending. That's not too expensive and is fairly easy to get going. Patent Pending won't stop everyone either but it will make then thing twice and maybe pass over you on to someone without a Patent Pending. Google it.

Let's face it, none of us are going to get rich printing the next best GoPro housing, one-at-at-time and home and shipping them. So for 99% of the stuff on Thingiverse, it's a non-issue. But there are some good ideas there that make me cringe when I see them. They are good ideas and should not have been made public. They will get taken away so fast.