When I recently sent out the inconvenient truth video to friends, what I heard back was nostalgia. Parents want their kids to learn math the way they did.
Their ultimate fear is that the new-fangled techniques might make their kids computationally incompetent in a dreamy quest for understanding. Most parents I speak to seem to suggest that they are willing to sacrifice mathematical understanding for computing prowess. Educators seem to want to go the other route- for them computational skill without understanding is useless.
The underlying rationale each group is also fascinating. Parents crave for a pre-calculator era when math involved doing long division by hand. Educators seem to be saying that computation is less important in today's milieu.