Who runs OpenSSL? Is it again volunteer? I think big companies need to step in and help creating infrastructure for these big projects.

Yes, all-volunteer. There are no ongoing commercial sponsors for that project.

As it should be. There was a story in HN a few weeks ago about why open source projects better not run on funding. Something with making it obligatory to work on the project and add features just to do something. And of course the people "donating" have some say in what's going on. I'm not saying backdoors per se, but should we want any sort of pressure this way?

Sounds like there is a need to sponsor OSS writers and not the actual projects. Kind of like having tenure but of course it would have to be voluntary, merit-based, etc.

This seems to be based on the humorous idea that big companies provide better security.