grammar - Does the ending to this sentence need an extra verb?

My sentence is as follows:

I lodged a complaint with Acme Corporation, a private entity.

Does it need to be changed into:

I lodged a complaint with Acme Corporation, which was a private entity.

I appreciate the meaning between the two sentences is slightly different. I would just like to know if the first sentence is grammatically correct. It looks correct to me but I have been told that only the second version is grammatically correct. Is there a 'rule' governing this situation that I can reference?

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