What BB told me:

If we blend as in that tutorial, we do:

A: Blend(S, T * S, f) = (1-f) * S + f * T * S

If we use Texture_Strength equal to f, we have:

B: S * Blend(1, T, f)

I will now prove that these two setups are the same:

B
{ substitute definition of B }
= S * Blend(1, T, f)
{ substitute the definition of Blend }
= S * ((1-f) * 1 + f * T)
{ (1-f) * 1 = 1 - f }
= S * ((1 - f) + f * T)
{ distribution of multiplication over addition }
= (1 - f) * S + f * T * S
{ definition of A }
= A

Voila. B = A.