HRH was seen doing his duties Tuesday in and around the London area -- including meeting with Korean War vets at Buckingham Palace ... where he hosted and chatted with the heroes, and later in the day, swinging by Windsor Castle ... where he was spotted exiting.

As you can see by the pics ... Chuck is very much so still with us, and the reason that's significant is because several Russian media sites and blogs floated a wild story about him supposedly kicking the bucket all through the weekend -- something that clearly isn't true.

These false reports were so rampant, in fact, that a BS statement being attributed to Buckingham Palace made the rounds -- which appeared to announce his sudden passing.

The cause these fake Russian sites were referencing was cancer complication -- and it got so out of control, the British embassy in Moscow had to issue an official clarification on the record ... noting that the King was not 6 feet deep, and instead going about his business.

He's just the latest senior Royal to face wild conspiracy theories -- remember, Kate Middleton has been in the crosshairs of tinfoil hat types for several weeks now ... that is, until she surfaced herself in the flesh over the weekend in what's an obvious and clear sighting.

The Princess of Wales was out and about Saturday, walking on her own two feet and looking relatively health -- this after being sidelined for a few months following a surgery she had in January, which involved a procedure in her abdomen area. Unclear what exactly it was for.

In any case ... she's been subjected to a barrage of jokes and gossip, just as her father-in-law has in the past 48 hours.