That's also true. The interface is in fact much older than the piano, having first been used on harpsichords, clavichords, and (I think) pipe organs. If I'm not mistaken, the black+white keyboard we use today was invented around the 1400's. The piano itself dates back only to the 1700's.
I can see the argument for the keyboard being a timeless UI because it's lasted mostly unchanged for about 600 years now.
I can also see the argument that 600 years isn't that long in the scheme of musical instruments. We've found ancient flutes from at least 30,000 years ago. The lyre, popular in ancient Greece, is not that different from a modern harp. Lutes are thought to have been present in Mesopotamia around 3000 BC.
Site note - I was surprised to learn that Bach lived before the piano became popular and apparently did not endorse the instrument until a few years before his death [1]. He would be familiar with the interface from earlier instruments, though.
[1] https://en.wikipedia.org/wiki/Piano#Early_fortepiano