If that person is wearing an air force uniform and you colourise it to look more like an army uniform, or a different country's uniform, you've made it less accurate as it looks like they're in a different branch of the military.

If you've got a photo of someone whose hair was white from age, and you colourise it as blonde, you've made them look younger and maybe given them a hair colour they never had.

If you've got a photo of a famous scientist or war hero who had a Mediterranean complexion and you colourise them with more of a pale complexion, you've made it less accurate as it looks like they're a different race.

(Of course, these sorts of accessibility-accuracy trade-offs aren't unique to colourising photos - they also apply to everything from translations of historical documents, through illustrations and selecting what content makes it into books, to questionably accurate history facts shared on social media)