Rogers had a relationship with Grigsby-Grunow and in 1928 Rogers-Majestic was formed.
Here is a time line and some info.
This article says Rogers was first with the spray shielded tubes. No reference as to where the info was obtained, though.
Here is info on the relationship between Rogers , Kellogg and Mcullough in tube development. Scroll both ways to read story.
I can’t find the patent on the spray shielded tube. But from my research I would say that all parties involved worked together, for these accomplishments to take place.