I think there is some confusion. RunBasic and LibertyBasic have no connection, from a programmer's point of view. LibertyBasic is great for Desktop/laptop applications, and RunBasic for internet based applications. LibertyBasic programs do not run in web pages, with or without RunBasic. This is clear from the documentation for the programs.
Why not try it out for free? This will make things clearer. There are versions that run locally on your own computer available from www.runbasic.com