I don't really get this argument. It's always made as if the taxes are applied in a vacuum where market forces no longer exist.
If corporations are operating in a competitive market, they will seek cost advantages and continue to compete for market share. Raised taxes represent an additional expense (for the purposes of this discussion), much like raised energy prices. It is not always the case that these costs are passed on to consumers. Rather, smart companies seek to become more efficient, reduce costs elsewhere, or even realize a slightly lower profit margin per unit in order to maintain or increase market share vs. other competitors.
There's also the option to reduce executive compensation, decrease shareholder dividends, and a host of other options available in the interest of remaining competitive. A smart company could actually outmaneuver other competitors, wind up with more volume, realize the same net profit after taxes, and pass lower prices on to consumers.
I mean, there are just a ton of other variables here. And, those who advocate low or no corporate taxes are frequently free marketers. So, it's very interesting to me that they all but completely ignore very relevant free market mechanisms that can countervail the effects of raised corporate taxes.
IMO, it's just an oft-repeated meme that "higher corporate taxes are automatically regressive because they automatically create higher prices for consumers".