Not always true. It depends on the price demand elasticity curve and margins.

Imagine Acme Inc selling Widgets at $100.

If taxes go up, the company's first instinct would be to increase the price. This works for some markets and products. However, if the customers and market are sensitive to price, they will lower or stop their consumption from Acme Inc. or move to competitors or substitute products e.g cooking at home instead of restaurants. In that case, Acme Inc has to pay the taxes out of their profits, assuming their profit was high enough, which results in lower profits, or takes losses and go out of business eventually.