OK, now here is where the true geek comes out.
It was never actually sang this way. See the capitalized letters.
During the first season, it was sung by professionals, who sang both pronouns as "they," but by Season Two, the Brady kids sang it, and both pronouns were sung as "we."
OK, my geek-o-meter just went up again. (Not that is ever considerably low being a 14-year member of this forum... and especially this month, headed to a certain expo next week that will feature both Disney fans and Star Wars geeks on full display...) ;-)