It is precisely what heads of state do, both centuries before Napoleon and since then through the present day.

Do you really believe the British press at the time was scrupulously honest? Or that Joseph II or Leopold II or Francis II allowed the unvarnished truth to see the light of print in the Hapsburg domains? Or Alexander I permitting an uncensored press in Russia?

And I wasn't aware that there were "bulletins" until at least late 1804, certainly not during the First Italian Campaign. Reports, yes, bulletins, no.