Parallel requests can be served, but they are all through a single instance and the abstraction gives you effectively exclusive access to the data store while the stateful part of a request is being processed.
In fact, you may find a traditional database behaves much worse when everyone is trying to modify the same row: if many clients do a read-modify-write at the same time, all but one of them will fail with transaction conflicts and will have to start over. If you aren't careful this can easily be O(n^2) total work done.
With Durable Objects, because your application code itself runs serialized in the object thread with zero storage latency (assuming cache), it's easier to make each operation "atomic" and avoid transaction conflicts entirely.