The problem could be that they actually are willing to do it for $10, but it's a low-status thing to admit.

If we both lived in the same appartment, and we both pretended that our time is precious that we are only willing to clean the appartment for $1000... and I do it 50% of the time, and you do it 50% of the time, at the end none of us gets poor despite the unrealistic prices, because each of us gets all the money back.

Now when the third person comes and cares about money more than about status (which is easier for them, because they don't live in the same appartment with us), our pretending is exposed and we become either more honest or poor.