Well, it’s not that Hindus consider the statue (the murti) itself to be the deity: it’s a manifestation of the essence or spirit of the deity depicted. Anything done to the image is not done to the statue itself, but to the deity. So when Hindus do things like making offerings to a murti or bathing it or whatever, they’re not doing that to the statue - the metal, the stone or whatever - but to the deity in question.
There’s a song from an Indian (Tamil) film which explains it rather concisely: “whoever sees the stone (i.e. the statue) does not see god; whoever sees god does not see the stone.” (This is actually seems to be a sort of homage to a traditional Tamil saying: “When a stone is seen we see no dog, and when a dog is seen, we see no stone.”) What the Hindu devotee sees is not the image, but the god who is made manifest in a way by the image.
The Hindu understanding of their images is actually a bit close to the Eastern Christian theology of icons IMHO: icons being “windows to Heaven,” not only representing the subject depicted but actually makes him/her present by participation in its uncreated energies or grace (this makes icons not mere sacred art, but something that makes the saint really ‘present’ in a way).