I took their meaning to be that at any large company you work in a pretty niche area because there are so many other employees. You get used to "not my problem" which isn't an attitude that makes sense in small companies.
The problem though is assuming that the majority of jobs are with small companies. Although 99% of US businesses are SMBs, only 45% of employees in the US (from quick Google checks) work for SMBs. So the majority of jobs are at large companies and I don't think FAANG would be so much a penalty (except for that you might have compensation expectations that don't fit these companies).
The point is that an engineer at a FAANG likely owns a miniscule fraction of the stack, whatever that may be. The average company doesn't need or want someone who is so deeply specialised.
This is such a ridiculous notion to be that I find a hard time lending it any credence. The reason average companies pass on FAANG is generally that they can’t afford them. Not “oh, this guy isn’t Jack-of-all-trades enough, we’re really looking for a midrate web contractor that still uses jquery but also knows some SQL”.
There's an entire world between FAANG and what you described. Most places will want something like this:
"We need two or three seniors who, between them, can handle the fact that our cloud resources are split between AWS and Azure 80/20, who understand security well enough to enforce least privilege for users, can write reliable if inelegant code in bash, python, golang and - when we have embedded stuff - lua. We'd also like people to be cost aware since we aren't made of money, and to be able to take ownership of CI, observability, logging, k8s in the form of EKS, a few VMs, and some difficult to change legacy stuff. Plus, provide the devs with a sensible local environment to work in that is as prod-like as you can make it, mentor a junior or two, wrap everything into some kind of infrastructure-as-code setup, present options to architects who are sometimes operating outside their field of expertise, and run the standups a d retros when your manager is on holiday"
The problem though is assuming that the majority of jobs are with small companies. Although 99% of US businesses are SMBs, only 45% of employees in the US (from quick Google checks) work for SMBs. So the majority of jobs are at large companies and I don't think FAANG would be so much a penalty (except for that you might have compensation expectations that don't fit these companies).