You are correct, the energy absorbed must be dissipated.
The absorbed electromagnetic waves are transformed into heat in our bodies (no other mechanism has been found for non-ionizing radiation). Tiny, tiny, tiny amounts of heat - so tiny in fact, that it is not possible to measure them.
Lucky for us, nature has armed us (and all other vertebrates amongst many other forms of life) with a system to dissipate the heat we absorb from our environment.
That system works quite well, which allows us to live and function in climates ranging from 50 Kelvin below to 20 K above our body temperature.
Also, lucky for us, scientists are in general smart and honest people, doing the best they can, and bringing us incredible knowledge.
On the other hand, we of course also have people who just decide for themselves, make up facts as they go along, and enrich small factoids with their own flavor of misinformation; but such is life.