Wiggins' comments came during the shortened 124-kilometre flat stage from Abbiategrasso to Asti, after riders had protested following a Thursday evening vote in favour of shortening the 258-kilometre stage by team's Professional Cycling Association (CPA) representatives.
The stage start in Morbegno near the French border was a chaotic affair as riders negotiated with Giro organisers and UCI commissaires. Eventually, after an eight-kilometre rollout, the peloton boarded buses for the 130-kilometre journey to the new start.
Wiggins appeared on British Eurosport partway through the shortened stage, eventually won by CCC's Josef Černy from the breakaway, to rail against just about everyone involved in the race, insisting that the riders have a responsibility to entertain the public.
"The whole thing is just a shambles," he said. "I think everyone ends up looking pretty stupid. Obviously, I'm talking from the perspective of someone four to five years into retiring. Let's make it clear, back when I was a rider, I would've been the first to not want to race in the race.
"But from the other side of the fence I realise just how much of a privilege it is to be a pro cyclist. The riders are every fortunate – and they deserve it – in terms of how much they get paid these days, and also the current climate around the world at the moment, cycling is very romantic and it's a passion and escapism for many people from the strain and pressure of daily life.
"I think riders do have a responsibility to ride and that's why they're elite cyclists because it's doing something that normal people perceive themselves as being unable to do, something of this magnitude."
The stage would have seen the riders tackle an eighth stage over 200 kilometres in length in less than three weeks, and the rider protest was far from the first complaint of the Giro.
Groupama-FDJ rider Jacopo Guarnieri has been among the riders to complain about the mammoth transfers between stages and early starts, while several riders have protested about the state of the Giro's anti-COVID-19 'bubble'.
Nevertheless, Wiggins added that, in his view, cycling fans and the general public were the ones who were losing out.
"The riders – to protest the way they did – with no unity as usual, nobody seems to know what is going on. The race director [Mauro Vegni] threatened that someone will pay for this on Sunday. The only ones who end up losing out are the general public and the viewers.
"I can see everybody's point. The rider's point – do we need a 258-kilometre stage the day after the Stelvio stage? The race organisers are happy to cut a day like tomorrow down, which impacts on whether someone like Tao Geoghegan Hart can attack and win the race having dropped Wilco Kelderman yesterday – 'we don't want to cut this but we're happy to cut that'.
"The whole thing just shows the lack of unity, the lack of organisation and the lack of power the riders have as a group. The union doesn't act as a union – can we say 'willy waving contest' here?"
As well as criticising the organisation, the Briton joined race director Mauro Vegni in criticising the riders. Vegni threatened legal action against riders if they didn't show proof that their proposals to shorten the stage were made before Friday, adding that "someone will pay for this."
Wiggins compared the riders' problems to those of soldiers and healthcare workers, evoking a trope unfavourably comparing the pay of public sector workers to that of professional athletes.
"To ride your bike for 250 kilometres for six hours – if it's in the rain or not – it's a little bit disproportionate to what some people have to do, like the front line in the army, working in the NHS in the current climate.
"That's why I see this as a privilege. Lots of people sat in offices ride their bikes at weekends for passion and love for the sport, that's why people fall in love with this sport because of what these riders have to go through.
"We're lucky to have a Giro d’Italia this year. From that respect, make the most of it. We’ve seen what it’s like when there’s no races.
Wiggins concluded his statement by opining that the riders' protest in Morbegno had been stronger than the rider-organised statement against racism at the Tour de France, where the peloton donned masks emblazoned with anti-racism messages.
"To add to that as well, they've made more of a stand today, more of a protest than they did for Kévin Reza and the stand against racism at the Tour de France. That's all I'll say on it."
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