Sorry, no! What they are called around the world does not make it correct in any way.
Solothurn was founded in the second half of 1929. As we all know the first model of the 20x138B weapon was the MG C/30 and Flak 30. The development of the Rheinmetall weapons goes back to at least 1928 (and maybe even earlier).
Solothurn only developed the AT rifles, nothing else.
Also we shall not forget that Solothurn was marketing Rheinmetall made weapons (for the reason you gave above). Namely the well known and undisputed 37mm Pak and the 81mm mortar made by Rheinmetall are advertised as Solothurn weapons. Nobody so far ever claimed these to be Soloturn developments or products.
The Solothurn designation originates merely from post war publications written by people who lacked this information.
There are many examples for such errors in ammunition history where information was hard to find or people just liked to use the name of a well known weapon instead a correct designation.
For this reason I never get tired to tell correct designations since in particular we as people with at least some little knowledge have to stick with correct designations. Bending backwards and using incorrect names to please ignorant people who want to keep their old and wrong knowledge can't be our aim.
Last but not least, the Italian M35 Breda is also a Rheinmetall development which got licenced to Italy.
A good friend of mine is currently writing a book on these weapons and the cartridge. I hope it will be out in the next few years. Plenty of facts and info then to be recognized.
Interesting,lets see the final book.That book makes for example 1940s army manuals here in Finland trash material.IF it is fact book.And it was Finland who used actually very first models of 2cm Flak 30,serial numbers for the guns delivered to Finland were under 150 on all known examples which survived the war and are in museums/collections now.
Base design for 20x138B was Erhardt Flz.K(20x70RB) airplane cannon round which was reworked/up calibered.
That newly designed caliber was designed to be used in Dreyse MG design which was also reworked/up calibered by designers Fritz Herlach and Theodor Rakula(who worked to firm Rheinmetall,but at the time in Switzerland).FIRST working guntype for this caliber was Solothurn S5-100.Rheinmetall sold this guntype before WW2 under name 2cm Machinenkanone ST 5 and two different variants 2cm MK ST 51 and 2cm MK ST 52(you can understand what ST means on the name).Guns here in Finland are all Rheinmetall 2cm MK ST 51 models,which together with 2cm BSW Lafette are known as 2cm Fliegerabwehrkanone 30(and also was original german designation name for 2cm Flak 30 -> 2cm MK ST 51 GUN+2cm BSW Lafette=2cm Flak 30.
It is CLEARLY MARKED INTO 2cm Flak 30 barrels 2cm MK ST 51.I can post you pictures if you dont belive,it is SOLOTHURN who owned the gun design,Rheinmetal owned everything else.
Even Americans tested that guntype but did not take it to their use.First operational user in 1930 was Kriegsmarine under designation 2cm MG C/30L.German navy used 2cm MK ST 51+Sockellafette 30L which together was known as 2cm MG C/30L.That is where you are right: ...First model of the 20x138B weapon was the MG C/30.
You are mixing gundesign with gunnames/models.And second: You are very wrong that Solothurn only designed Antitank guns.Solothurn designed guntypes which had universal usage: Antiair,Antitank,Vehicle guns.Even german 2cm Kwk tankgun is based to Solothurn design.
And as we all know,later updated version 2cm Flak 38 was designed by firm Waffenwerke Mauser AG,not Rheinmetall.It increased firing speed from 250-300rounds/min to 450-480rounds/min and was lighter.
btw,here is my friends M35 Breda.It is nice gun,but i personally dont see german design in it.Its firing rate was slower 200rounds/min and interior design is totally different.Flak 30 uses rotating breech block while Breda have sliding breech-block.