You're eliding the most important part of the definition IMO: a plan to reach profitability with the initial investment alone. YC never expects its companies to become profitable with their investment alone, nor should it - it's designed for growth companies that will receive multiple rounds of funding over time!
But when YC invested $120k for 7% equity, we typically didn't call all those startups like Dropbox/AirBNB etc "bootstrapped companies". And $180k for 2 founders is more than YC's previous terms.
>If one further gatekeeps the label with
It's unfair to call it "gatekeeping" rather than a case of confusing many readers with a headline that flips the meaning of "bootstrapping".