Googling around, I found that this info indeed appears on some baby name websites, but as far as I could see not on a reliable one.
I think the meme of a connection between
Muriel and
Mariel is something that is just bound to happen, like some inevitable folk etymology.
There is also a quite successful film called "
Muriel's wedding" where the switching between the names
Muriel and
Mariel seems to play an important role, which may have enforced the perceived connection between the two names.