Yup, dead wrong.
How do I know?
https://www.youtube.com/watch?v=4GYRGafQ7SI
Yup, a 1959 episode of Bonanza gives the full account of how the Cartwright clan helped (an oddly mid-40s guy who in no way resembles the actual young Sam Clemens) the young reporter to come up with his pen name.
It must be historically accurate because it is a TV western, and they knew a lot more about historical facts then than we do nowadays.
Sorry you went through all that effort, Kevin, but Hoss beat you to it!
Carl
😀