Right but I would think you'd also need to avoid the executor learning that you were accessing the same record at different times. Merely encrypting the records wouldn't prevent this, so your query (to be homomorphically encrypted) would need to be executed in such a way that you look at more than one record.

You'd need that to stop the risk that, say, an attacker learns (from a side channel) you were looking for person A's details at time T1, and thereby unmasks which other queries/times were about A.