I don’t think that’s quite true. This is oversimplifying, but let’s assume that companies are profit-maximizing and are in a perfect market. Even if we start taking some portion of their money away from them, it doesn’t change what price will maximize the remaining portion of the profit. If a company raised its prices, it would lower its total profit, regardless of the portion of that profit we are taking away.
I would be far more worried about companies leaving the US, losing investors, or facing competition from smaller companies that are in lower marginal corporate tax brackets but are not necessarily more efficient. In other words, it is an issue of the long term viability of American industry, not directly of consumer prices.
However, if we levied a per-unit sales tax on these companies I would agree with you.
It seems that you are arguing that corporations will pay the tax, not individuals. In the short run, I agree that corporations may not be able to pass on the increased costs of taxation. In the long run, the entire industry will adjust and the costs will be borne by the consumers. Corporations that do not pass on the increased cost will fail.