teD>I also laooked up right in OED -- goes on for pages, and I scanned quickly without coming up with right as rain.

here's what having a searchable OED turns up:

14b. In good health and spirits; sound, well, comfortable. Now chiefly Austral. and N.Z. colloq. (influenced by all right: see sense 15c below), exc. in various colloq. phrases, as right as my glove, ninepence, rain (see also sense 15a below), a trivet, etc.

15a. In a satisfactory or proper state; in good order. to get+right, to set in order. to make it right, to square or settle matters. Also in colloq. phr. right as rain (see also sense 13b above).

FS>All Micheal's website does is raise more questions for me: e.g. "right as a trivet"?

that does indeed sound strange, but explaining 'right as rain' as an alliterative variation on a theme sounds quite sensible.