The band had to axe two gigs in mid-May (16) after Kiedis was hospitalised with stomach problems, and the 53-year-old subsequently revealed he had inflammation in his guts, which was complicated by a recent stomach virus and existing scar tissue from previous hernia operations.
But some critics weren't convinced by his explanation and took to social media to suggest Kiedis' health troubles were linked to his past substance abuse issues - something he last struggled with in 2000.
The rocker was quizzed about the speculation during an interview on Australian TV show Sunday Night, and insisted he was unfazed by the gossip.
"I felt more care than anything else," Kiedis said of the fan response to the drug rumours. "I got a lot of messages in the mail; it just seemed like people did care. My friends called, people I hadn't spoken to for years called, but what people assume or think about using (drugs), I could care less. It didn't faze me at all."
He added: "I happen to love being sober, I also loved being wasted at times. Being sober for me is a pleasure, I get a lot of joy out of it; it works for me. I get to surf, I get to hang out with my son, I get to play music, I get to be OK."
Kiedis also touched on the night of his hospitalisation, recalling, "This was knocking me off my feet, and I was white as a ghost, and my whole gut section just seized up, and I was kind of falling to my knees in pain, so I got taken by a friend to the hospital from the gig."
However, the singer is now firmly on the mend and he mused, "Maybe there was a reason for me to get sick, so I can get stronger than I was before."
Kiedis will be keeping busy for the next few weeks as the Red Hot Chili Peppers prepare for the release of their new album, The Getaway, on 17 June (16).
The band will continue its tour in Europe on Saturday (04Jun16), when the rockers perform at the Rock am Ring festival in Germany.