Joshua was present to promote his upcoming title defence against Alexander Povetkin at Wembley and it was during that pair's fairly cordial face-off that Miller piped up.
Povetkin (34-1, 24 KOs), 38, tested positive for the banned substances meldonium in May 2016 ahead of a scheduled fight with Wilder.
Povetkin then tested positive for ostarine, a muscle-builder that has been on the WADA banned list since 2008, in December 2016.
He was suspended from WBC-sanctioned fights after the second failed test, but appealed and was allowed back into the sport with a year-long ban and a £188,000 ($245,000) fine.
Since then he has twice failed dope tests but reaffirmed his threat in his last fight, on the undercard of Joshua's win over New Zealand's Joseph Parker on March 31, when he knocked out England's David Price.
The IBF, WBA, WBO and IBO world champion has been criticised by certain parts of the boxing community after he was forced to disregard a unification bout with American champion Deontay Wilder to organise a mandatory defence against Povetkin. But for the moment I'm concentrating on beating Povetkin, who is a good technical boxer and a unsafe puncher'.
But Joshua, who insists on a rigourous testing regimen for himself and all his opponents, says: 'If I missed a test or was even an hour late for one people would say oh, he must be doping.
Joshua is phlegmatic, saying: 'I am not the lawmaker in this.
"People talk about me, then see me face to face, and they still want to talk", Joshua told Sky Sports News.
The ban has since been lifted and Povetkin came to London on Wednesday to pose for pictures on the Wembley turf with Joshua, who accepts that his reputation would be damaged irreparably if ever he was caught doping. Or someone is better than you on the night, give them the respect and bounce back.
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"I would rather stay clean and give it my best every time. I have got to kick them back down". Alexander Povetkin in a past match.
Miller will first fight on October 6, live on Sky Sports on the first DAZN show, as he bids to further draw Joshua's ire.
It is landmarks like this which have brought Joshua to the point of saying: 'First I was fighting for fun. I have been justified.
"For me it was very, very suspicious". I don't know what happened but at the end of the day, all I can say is that I was accused of wrongdoing when I wasn't.
"First I was caught on meldonium, and it was a nanogram quantity. I am clean and I know that I was clean then".
'I have earned the right to this fight by beating the other heavyweights to become Joshua's mandatory.
"Does is sound realistic to you?"
"The amount they found doesn't give any affect so why would I ever want to do that".
"I have nothing to do with it, and I am very well deserved of the fight I am getting". Povetkin admitted he used meldonium, but said he used it in 2015, not after January 1, 2016 when it was banned by the World Anti-Doping Agency.
Forty seven Russian athletes and coaches were banned from this year's Winter Olympics after an investigation into state-sponsored doping during the 2014 Games in Sochi.