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The only thing i can think of is that because it contains moving parts, it should be able to move slightly within the case.
More likely though is that its one of those silly pieces of advice, like not using a mobile phone in a petrol station.
Very important, screws for mounting drives are not the same as your regular screws, they are shorter and have finer threads, shorter is important so don't subsitute other types. You may get away with it with the bottom mounting, but longer screws in the side may damage the drive.