I just put the third battery in my 2000 EX...65k miles.

Honda (or Sears for that matter) can do a simple check of the battery charging power, alternator and starter. They will let you know if any components are weak.

Is this what is stated in the TSB no. 02-034?
I don't think that is from the TSB - I think it is from the news letters sent to Honda techs...