I don't even think it's a case of trusting them, because if they get access to webcam data or something else that they shouldn't, assume someone with less well-meaning intentions can and has also done so.
The problem is that the normal, every day people who run these devices, on the most part, don't understand that not only are they open to the internet, most manufacturers provide Dynamic DNS making it painfully easy to search for them. Further still, these manufacturers set the same default password for every device. Some have been known to leave the "empty" credential slots usable. Due to poor programming, you could simply login with no credentials at all.
I have to agree, I'd be hard pressed to decide whether I would or wouldn't accept this "survey", but, with notice, like people are being given here, you can mitigate the risks (cover the cameras, remove the data etc) and be told there are weaknesses in your system, or alternatively, not know and have some unknown accessing them at any point they wish, for any reason they wish.
In several countries pen testing tools for plebeians are even illegal.
But, lets be reasonable for a second, Japan is concerned that if people's networks aren't secured before the Olympic games, these vulnerable devices will be used to disrupt systems by outside attackers and potentially costing the country significantly.
It's well known that IoT devices on the market are poorly implemented and poorly secured and rarely-to-never updated by the manufacturer.
It is particularly hairy, and I don't think there's a perfect solution for the average person.
Once the avalanche is in progress, a government plan to add an extra snowflake scarcely matters.