That may be true in many places, but the Swedish forestry industry is very big, and the district heating plants really do burn mostly forestry byproducts. Of all the biofuel used in Sweden (not just for energy generation), 75% comes from forestry products, and the vast majority of it is either unrefined wood products or byproducts from Kraft process paper manufacturing (like tall oil and turpentine etc).
Specifically in district heating, 87% of the forestry-sourced fuel is unrefined wood products. Almost half of it is just bark, branches and treetops. Of all the biomass in an average mature tree logged in Sweden, 43% ends up as pulpwood, 43% as saw timber, 8% gets burned for fuel and the remaining 6% is treetops and branches which also tend to end up burned for fuel.
There is definitely a lot of debate in Sweden about sustainable forestry practices, though. The industry really wants to clearcut everything for convenience, but it's really bad for biodiversity and the general public hates it.
Source: the report Hållbarare biobränsle i fjärrvärmesektorn, Energiforsk 2023; specifically the charts on pages 14 and 15. Link: https://energiforsk.se/media/33316/2023-979-ha-llbarare-biob...
Addendum: I believe there's also been some studies and experiments involving importing olive pits from the Mediterranean olive oil industry for burning in district heating plants, but I don't think it's been done at scale.