Personally, I don't work on open source software. My personal projects are public, free and open source but they are useless to anyone other than for me.

The main reason I publish them publicly is ... I don't know why actually. However, one benefit to public github repositories is I can try out various services that are free for open source projects. This way I have exposure to these services which is nice. Also it is easier to get help from others or ask questions when I get stuck.

In my experience, I've found programmers very helpful as long as I am willing to put in some effort.

For me it looks very similar to training. they want you to have x, but don't provide the ability to acquire x to their employees.

What do they think will happen if you do work on open source software while in their employ?

Most likely nothing, but most companies seem to have the expectation that OSS has to take a backseat

Yea. Give me free code, don't make free code is a common problem.

Your employment contract could stipulate that any programming done outside official work is owned by the company. A “work for hire” of sorts. Whether these “copyright assignment” clauses are legal depends on your jurisdiction.