True, but it doesn't matter what the company is like. When people look at your resume in the future, be it on paper or on LinkedIn, they notice the names. Having Big Names on your resume is significant, and anyone applying for a job involving Linux is applying for a job at a company that knows Red Hat and probably uses their enterprise products.
In the end, a resume is all smoke and mirrors anyway. Accurate, yes. Truthful, yes. But market-speak just the same. It has no relationship to your ability to do things in the future, all it can ever do is summarize in hyper-compressed form what you have done in the past, in a context your future employers probably don't have, where the hyper-compression necessarily takes out much of the essential information as to what the starting point was and how the end point was achieved from there.
The employer knows this just as well as you do. So employers pay a lot of attention to brand names, in the hope that vendors with a good reputation to uphold will have hired and/or kept on employees who help maintain that reputation.
Again, this goes back to Marketing 101 - it doesn't matter what you know, it matters only who you know. (Which is why industry is such a mess.)