The only perfect password solution is the one you have complete control of the total solution. In the real world this doesn't exist for most of us and we have to select a solution that works for us.
Because you can share a site only proves that there is a way to the ability to connect to a site that you select with your credentials with individuals you trust. Here is how it is done
You're right, they could all have phone home solutions, actually storing your unlock code would be sufficient, and be hosted by the NSA. If that is the case you'd be better off staying off the Internet all together and investing in tinfoil. LastPass has been very up front in how their product functions.--
"Progress isn't made by early risers. It's made by lazy men trying to find easier ways to do something." - Robert A. Heinlein