He's a draft dodger.
In 1969 I was a draft dodger.
I received a draft notice which I totally ignored, did not respond in any way.
The reason was, I had already enlisted and was serving in basic training -- boot camp.
I figured there was zero chance my draft board would track me down to serve notice while I was already serving, and of course, they never did.
My guess is something similar with Denys Davydov.
Ukraine's government cannot be unhappy with the work he does reporting on war results.
In any national draft system, many are granted lawful exemptions, and so claims that Davydov is a "draft dodger" come from no specific knowledge of his actual legal status.
I think such claims simply reflect the anger and frustration of our pro-Russians at the popularity and effectiveness of Davydov's work in defense of Ukraine.