Steph, Those are the requirements for being given a visa. You are not eligible for visa waiver travel if you have ever been arrested - you don't even have to have been convicted. And the fact it is spent makes no difference. Your partner would most likely be given a visa but he is not strictly speaking eligible for the visa free program.
Having said that I would agree with him - how on earth are they going to find out? I would say the odds on him just being allowed in are exgtremely high.
If you want more info about the visa waiver program the UK site is here:
http://www.usembassy.org.uk/cons_web/visa/niv/vwp.htm