I think that assertion deserves to be examined a bit more closely.
We are already effectively subsidizing the fossil fuel industry to the tune of 5+ trillion USD per year [1]. This is a figure from the IMF that includes direct monetary subsidies as well as externalities like public health, environmental damage, etc.
So the question now becomes this: would switching to renewables cost more than that? If we started dumping that same amount of money into renewables and corresponding infrastructure, how quickly could we switch away from fossil fuels? If we do some impromptu calculations based on current cost of solar panels, batteries, etc., it seems like it might take maybe 20 years.
Obviously it's not that simple in practice, but I think this demonstrates that humanity could theoretically switch away from fossil fuels without enduring any severe hardships. This isn't a problem of the technology not being good enough[2], or renewables being too expensive: it's just a political/organizational problem.
[1] http://www.imf.org/external/pubs/cat/longres.aspx?sk=42940.0 [2] With the possible exception of jet planes, for which batteries aren't good enough to provide a compelling alternative yet. But I would guess that when the electric car market really starts to take off, battery tech will start improving a lot faster.