> The first mechanical dishwashing device was registered for a patent in 1850 in the United States by Joel Houghton
> The device was both slow and unreliable.
> Another patent was granted to L.A. Alexander in 1865
> Neither device was practical or widely accepted.
And finally
> The most successful of the hand-powered dishwashers was invented in 1886 by Josephine Cochrane together with mechanic George Butters
(https://en.wikipedia.org/wiki/Dishwasher#History)
So yeah, all three invented the dishwasher it seems, but thanks to Josephine Cochrane (and Butters), we actually have a working and reliable dishwasher, something Joel Houghton was unable to build.
You're all right, in your own way.
However it seems those early dishwashers where pretty different to modern ones, least of all not being automatic: https://www.homestratosphere.com/dishwasher-history/