for all we know it may be using part of the metal body to pass either + or - 12v to the lamps.
Provided the other side of the 12 volt is not already earthed then earthing one side would not cause any more problems than earthing one side of a battery in a torch.
If the instructions are not clear or in another language as they often are then contact the retailer or manufacturer to clarify or use your own good judgement. Just because its metal or has a metal case doesn't mean it "has" to be earthed.
I do use my own judgement based on over 40 years experience of electronics 30 of which have been in designing equipment. And investigating failure modes of equipment.
I will accept that the operation of some very poorly designed and cheaply built electronic "transformers" may be adversely affected if there is a capacitve coupling of their output to an earthed metal case.
If they are that sensitive then the design is poor and as a result I would be very concerned that the design would not fail safe in the event of a component failure. Fail safe being that no matter what failed the output remained free of any mains voltage.