As the OP wanted to thank you all for the lively discussion. My biggest takeaway is this is the grayest of gray areas. Many different interpretations and opinions. Here and elsewhere. Even my local FSDO punted to the Chief Counsel in DC (as Ron suggested).
Although I would like to lean/agree...
i am a student pilot initially pursuing my private helicopter certification. (commercial later) i work for a county mosquito control and also assist our sheriff's office on LEO ops. We fly public use (non-certified aircraft). Can i log my mission times towards my 40 hr, cross-countrys, etc...