Sorry, but I'll point out a bit of elitism in this post.
> (Unless if the job description is for front-end development only, in which I'm less qualified to say whether a CS education is needed or not.)
The browser is an extremely complex platform, at least rivaling an operating system. If you're going to argue that advanced knowledge of a platform is required for non-frontend work, you should be comfortable making the argument for frontend.
Except people generally don't make that argument. Frontend devs (I am not one) are looked down on. But it's a double standard.
I'm sure that wasn't your intention, but it's a constant expression I see - that web developers are a class separate from the rest of us. The truth is that OS knowledge is not critical and the general sentiment that frontend devs can do their job without understand the complexities of a browser only reveals this.
More to your point, I taught myself about OS's and x86 outside of class because I wanted to learn how to exploit memory safety issues. I never made a career out of it, but I learned a lot, and it was a matter of buying a few books and talking to people on IRC. I found tons of excellent talks by Herb Sutter and Scott Meyer about CPU architecture and how code maps to it.
There's a ton of resources out there for those who choose to self-teach.