Having worked on movies shot on video, color film, and B+W film, the lighting and design choices are very different. Colorizing BW movies makes some sense for historical footage where that was the only available option, like newsreels or very ear;y films, but for anything with aesthetic choices involved (German expressionism onwards), it's no more appropriate than trying to figure out what Picasso's models 'really' looked like. Artists are not that concerned with fidelity, but with pushing the salient characteristics of their available or chosen medium in support of a particular artistic vision. We are not merely recording; as soon as there is more than one option available (whether that's paint on canvas or different kinds of film stock) we start playing with the possibilities. When you begin colorizing you risk compromising that.

The 'exact' concept is wrong. Any picture depends on lighting, camera used, filters, lens, etc.

I don't mind colorized photos. Yet for some of them that were made thinking in a b/w result (For example, the 'With The Beatles' album cover) colorizing means the lost of those stylistic choices.

Agreed. Interpretation or not, I don't see a problem as long as the colorization is not outright inaccurate. Also consider that for a long time people didn't even have photos and only had illustrations and written descriptions to go on.