ELI5: How did riveted ships stay afloat?

So I know that one of the causes for the decline of shipbuilding in many industrialised towns was largely brought about by the changes to construction that Welding allowed which Riveting didn't.

But how did ships stay afloat if you've bored a hole through the hull and sealed it with a rivet?

Were the plates still joined with welding, and the riveting just used to hold the plates to the frame and sealed with lead or similar?