I find that actually quite controversial - correlation does not imply causation. The general sentiment within the community is that the causation works from the other side i.e being good at slow leads to being good at blitz.
Here are some quotes you might find interesting:
"Playing rapid chess, one can lose the habit of concentrating for several hours in serious chess. That is why, if a player has big aims, he should limit his rapidplay in favour of serious chess." – Vladimir Kramnik
"He who analyses blitz is stupid." – Rashid Nezhmetdinov
"Blitz chess kills your ideas." – Bobby Fischer
"To be honest, I consider [bullet chess] a bit moronic, and therefore I never play it." – Vladimir Kramnik
"I play way too much blitz chess. It rots the brain just as surely as alcohol." – Nigel Short
"Blitz is simply a waste of time." – Vladimir Malakhov