Only partly true, as you have to built the whole gasifier and system sturdier to deal with the pressure. All connections have to be really tight, as small leaks will lead to escaping gas. Different if you run on underpressure caused by engine suction.
Woodgas can be used with compression ratios (CR) up to 17:1 (Koen has a research paper in his google drive that stated this), so using a normal CR of a petrol engine with a slight supercharge on woodgas should be possible, as you won’t exceed the original petrol power.
See pages 227 to 229.
Book from Switzerland (written in German) pages 344 to 363