NO! The Symbian Alliance Formed because Nokia wanted to control its competitors to such an extent to make them never able to best Nokia. They did that by doing closed versions of Symbian that were never open to the Symbian Alliance.
That happened later, Symbian spun out of Psion. The first Symbian based phone was the Ericsson R380. The biggest difference between all the members were that the ones who took control of a UI built up more control. These were effectively Nokia and Docomo, hence why Symbian was used so much in Japan on their "feature phones" and S60 became strong.
UIQ used by many of the other manufacturers was never developed by any of them and was effectively an orphaned UI company.