Rogers had a relationship with Grigsby-Grunow and in 1928 Rogers-Majestic was formed.
https://www.hammondmuseumofradio.org/rogers.html
Here is a time line and some info.
https://www.broadcasting-history.ca/index3.html?url=http%3A//www.broadcasting-history.ca/station_groups/Radio_Television_Station_Groups-Standard_Broadcasting.html
This article says Rogers was first with the spray shielded tubes. No reference as to where the info was obtained, though.
https://www.ieee.ca/millennium/alternating_current/ac_halloffame.html
Here is info on the relationship between Rogers , Kellogg and Mcullough in tube development. Scroll both ways to read story.
https://books.google.ca/books?id=QNJGAFkdY40C&pg=PA79&lpg=PA79&dq=mccullough+tubes&source=bl&ots=g5t8JrkSLn&sig=2wEFydqQDaoBCUbhXdua4NNDmWs&h
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.
Bob