That gets repeated a lot but I have observed the opposite when you have a diversified company dogfooding an internal product that isn't strategic in their portfolio, or is targeted at a market segment that the company doesn't belong to. I have seen companies hamstring themselves by using a product that isn't the best offering for them or a poor technical fit, only because it is their own offering. Also, in the worst case, companies become develop tunnel vision in the market, because they don't regularly use the competition.
If you have a large, international software company targeting small to medium business customers in the US, dogfooding would be counterproductive. It would probably harm their strategic customer base by overcomplicating their product with features they don't need at the same time it slows the parent company down by using a product that's poor fit.