I didn't say the C64 and Spectrum were directly influenced by the BBC (though I can see why you read my comment that way) but that the wider industry was. eg Parents bought kids BASIC systems because schools had BBCs so the C64, whilst often just used as a games system, was bought because it was also "educational".

If it weren't for the BBC, I'd wager far fewer homes would have had BASIC-based micro computers and thus that industry would have been much smaller.