If you sell BRK shares, the money comes from the buyer, not BRK itself. It's a corporation, not a mutual fund.
And to play devils advocate to that: Berkshire probably almost generates cash as fast as they would ever buy back stock.
Another place where normal corporations would be affected by stock price is when they want more liquidity for operations via debt. This doesn’t apply to BRK because they already have a massive stockpile of cash. But stock price is not that isolated from company operations if a lot of investors start pulling out money (by selling stock).