The key distinction is whether you count the EV of a single wager, or the expected growth of compound returns.
As you say, the single-wager EV is independent of bankroll provided you can afford it in the first place. This is also what most people mean when they say EV, and indeed the common mathematical definition of it.
However, skilled risk takers know that the arithmetic EV isn't what matters more generally. What matters in the long run is geometric EV, or expected growth of compound returns.
And for geometric EV, bankroll absolutely matters. The larger your bankroll, the better your geometric EV. I suspect this is what the parent comment referred to.
(However, when the wager shrinks in comparison to your total wealth, the arithmetic EV approaches the geometric EV by Taylor series approximation. For "everyday affairs" (as I think Bernoulli put it) you can think of them as equal.)