Let's say that you know that someone stores documents by SHA, and silently overwrites collisions. Is there any way this would help to deceive them after being f

Let's say that you know that someone stores documents by SHA, and silently overwrites collisions. Is there any way this would help to deceive them after being forced to give them your data? It seems like once the data is out of your control, you can't match an existing SHA, and if you created a pair of documents that match SHAs, you can't predict which one will be overwritten.