Noticed train shifting coach inappropriately? (12)

I believe the answer is:

indoctrinate

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'noticed train shifting coach inappropriately?' is the definition.
I can't tell whether this definition defines the answer.

'noticed train shifting' is the wordplay.
'shifting' indicates an anagram.
'noticed'+'train'='noticedtrain'
'noticedtrain' with letters rearranged gives 'INDOCTRINATE'.

Can you help me to learn more?

(Other definitions for indoctrinate that I've seen before include "attempt to brainwash" , "change ideology" , "Imbue (someone) with an opinion" .)

I've seen this clue in The Times.

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