Yes, I have heard this, too...but Clint brought it to our attention that fish are infact cold blooded, so therefore, they just slip away. I also doubt that blood freezes in the fashion as it it thicker than water. I have used the clove oil method a couple of days ago, but the fish was already listless.
Well at what temperature would the fish slip away? According to a study I read, fish blood begins to crystallize at 28 degrees F, whereas water has a freezing point is 32 degrees F. It was the freezing point for those antarctic fish, but as you mentioned, blood is thicker than water, so even though bettas are antarctic fish, they're blood probably does not freeze at a temperature higher than the water would freeze. If they slip away before their blood began to crystallize, then I can't imagine that it would be painful because they're already gone.
Do you happen to know around what temperature they slip away?