Sorry, I do apologise. You are quite correct:
Note:Travelers with mental illnesses can travel visa free under the VWP provided that their condition does not render them a danger to themselves or others. They may wish to carry letter from their doctor to that effect to facilitate their entry into the United States.
http://london.usembassy.gov/add_req.html
However, having read this:
Travelers with arrests/conviction(s)
We do not recommend that travelers who have been arrested at anytime attempt to travel visa free under the Visa Waiver Program(VWP); they are required to apply for visas before traveling. If the arrest resulted in a conviction, the individual may require a special restricted visa in order to travel. The Rehabilitation of Offenders Act does not apply to United States visa law. Therefore, even travelers with a spent conviction are not eligible to travel visa free; they must
apply for B-1 or
B-2 visas. If they attempt to travel under the VWP, they may be refused entry into the United States.
So does that mean someone arrested under the Mental Health Act is not able to use the VWP?
I have done a search on Australian's sites and Canadian sites but cannot find anything relevant. Perhaps someone with more knowledge could intervene.
If you are planning on residing in these countries indefinitely then is the advise to declare everything correct?