It's a Catch-22. The Cultural Influence tech should give you both the Cultural Forum and Information Hub star base modules, but:
1) You can't build a Cultural Forum module because the required tech (Cultural Exchange) is incorrect.
2) You can't build any further influence modules based on later cultural tech because they are all predicated on the Cultural Forum module. (Which you can't build - see point 1.)
As Publius of NV points out, all .xml files are compiled into a .bin file when you start a new game. Thereafter, any saved game contains only the versions of those .xml files that were initially compiled (I'm pretty sure that includes mod folder files). Thus, changes to .xml files will not take effect until you start a new game.
Try the StarbaseModuleDefs correction in a new game and let us know what happens, eh? (Unless something bad happens, in which case we have no idea what you're talking about. Who are you? Oh, look, a velociraptor!)