Final Stages of interview - can HireRight find out if I was fired?

I was laid off my last employer who promised me that when future companies contact them - they will not be able to say anything but verify my position, starting / end dates. However, I was worried by reading some online posts that background check companies like HireRight can ask questions like "Would you rehire this person?" and my employer would have to say no. Is this true? Can they ever find out if I were fired?

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