Well, no.
A tax increase on income over $250,000 is not a "higher cost." The business owner's taxable income will remain the same. He can, of course, CHOOSE to increase his charge to customers by an amount that will increase his income to make up the difference. But you're forgetting that there are other, non-rich business owners out there competing with this one. The taxes of these other owners will NOT go up. Presumably, these other owner will keep their charges unchanged. So, if the "rich" business owner tries to increase his fees, he'll lose customers.
What will most likely happen is that that the rich business owner will hold the line on his charges to retain his customers, and he (and not his customers) will pay the increased tax.