Colin Renfrew (and others, like Peter Bellwood) have argued that the first farmers in Europe originated in Anatolia and spoke Indo-European languages, thus placing the Indo-European homeland in Anatolia.
I think that recent genetic results pretty clearly show that this hypothesis is wrong, but I would not call it at all crazy, at least not in its initial phase. Today it looks as if the first farmers originated in the very heartland of Middle Eastern agriculture, along the Turkish-Syrian border where we find the wild ancestors of most of the first domesticated plants. I don’t think that they went directly through Anatolia – it seems more likely that they settled Cyprus and various Aegean islands, on their way to Europe. That makes sense, when you think about it – their next-door neighbors probably weren’t far behind them, and it was easier to go around them and find areas that were either uninhabited or contained only hunter-gatherers, just as it was a lot easier for the Brits to conquer and settle North American and Australia than France.
Those early farmers probably spoke something distantly related to Basque. By 4000 BC, they’d occupied all of southern Europe (including Mediterranean islands like Sicily and Sardinia) and the central and western parts of northern Europe, as far as southern Sweden and England. If you had evaluated Renfrew’s hypothesis back then, you would have said that he was almost entirely correct. The problem is probably publication delay – the thesis was fine when first submitted.
Starting around 4000 BC, Old Europe suffered from new population movements that led to a huge population turnover in northern Europe and to lesser but still dramatic genetic and cultural changes in the south. Any turnover that big (at least 50% of the population in northern Europe is descended from people who hadn’t been there before 4000 BC) is likely to introduce a new language, all the more so since the process seems to have been ultra violent.
Anyhow, many people in the soft sciences are prone to be wrong because they’re crazy* – like those who know that there can’t have been conquests and migrations and ethnic cleansings in prehistory because the idea bothers them. But some are basically respectable people who just happen to be wrong. We’re all wrong some of the time.
* some are dumb, too, but that’s another story.