I think it's interesting to talk about how "act your size" can also be wrong. Sometimes fake-it-til-you-make-it is the goal. Contextually you should hold both ideas to be true and apply them appropriately.
Maybe you just thought the original post is a vague platitude and you don't want to give them the satisfaction but maybe we can share some of what we've experienced.
One thing I always think about is hiring generalists vs struggling to maintain departments you can't sustain. I understand businesses think this way, so it influences how I think about applying to roles. I'm currently in a generalist role and when searching I always look for smaller businesses because I find my impact is higher, and repetitive work is my greatest fear.
And sometimes they can both be useful at the same time. A while back I was contacted by a Fortune 500 company to build them some custom hardware. I'm the proverbial "one guy in a basement" so I could respond quickly to change requests without having to go through multiple meetings and their engineers appreciated that.
OTOH, as we got deeper into it, when I realized that they were planning to do most transactions by Purchase Order, I was really concerned about scaring them off by telling them I was really just one person, so I very quickly spun up an LLC in an attempt to look larger, at least to their Purchasing Dept. At the time I didn't realize that you can get an EIN (Employer Identification Number) while being a Sole Proprietorship, but creating the LLC just took a few minutes on the state Attorney General's site anyway.
This is a really interesting point, I think.
In my opinion, it depends on what your larger goal is. If your goal is to eventually become a big business, that changes your approach and "fake it till you make it" gains some validity. In a sense, those sorts of businesses are less "small businesses" and more "large businesses in their infancy".
