Snapedom

What I'm saying is that it is possible Walburga heard from Bellatrix that Regulus had defected and was killed on Voldemort's order.
Unlikely, because Kreacher firmly believed Regulus died loyal to the Dark Lord, so Walpurga in all those years never hinted at the possibility of a defection or disappointment about Regulus. She kept up the legend of her brave little hero in front of Kreacher.
During the 'short while' between Kreacher's return from the cave and Regulus death Voldemort might have suspected defection, but when he suddenly died, the only logical assumption is he was killed by the enemy or in doing something stupid to impress his master. Regulus may be one of the 'three dead in my service' Voldemort mentioned in GoF, Rosier, Wilkes and ? .
Sirius' conclusion is also perfectly logical from the opposite POV. Regulus disappeared, neither the Order or the aurors were involved, he was a soft idiot likely to chicken out, so it must have been Voldemort or one of his Death Eaters.
Regulus left his farewell note in the cave, pointless, if his defection was already known.