No. These would be crimes that Voldemort was suspected of being behind, probably without much proof because Voldemort was always good at hiding his traces, and it would be in his interests to be able to disassociate himself from his worst crimes so that he wouldn't alienate too much of the wizarding world. Thus there would be plenty of grounds for people to choose to disbelieve such allegations.

Leaving a great big skull with a serpent hanging out of its mouth behind whenever the Death Eaters killed doesn't sound like distancing themselves from their worst crimes to me.

Except that the DEs did not show their faces, right? They hid behind masks and there was no way to tell (without their wand) who cast the Dark Mark. So there was still hiding.

Yes, that illustrates my point. The wizarding world would know that some group of people were doing these crimes, but not with any proof who was actually behind them. As long as the Prophet is only able to report suspicions and rumours there would be plenty of scope for young potential death eaters like Regulus to believe that Voldemort was being misrepresented and unjustly accused in the press. The dark mark identified the act with a particular group, but doesn't identify Voldemort with that group, and Voldemort could have been like a typical film villain, with a moderately presentable public face while at the same time running a criminal organization behind the scenes, and it was only after he was defeated that his links to all these crimes was actually proved.