Yes, the lack of any act of the will on the part of infants is key.
To say that BoB can apply to infants turns the action of BoB into ex opere operato ... i.e. essentially into a Sacrament.
BoB has an interesting history. St. Cyprian, perhaps the originator of the notion, spoke of BoB as a SACRAMENT. Modern theologians cite this as an error.
But was it really?
Elsewhere, St. Cyprian says that BoB martyrs are "washed" in their own blood while angels pronounce the words.
So he saw it as an alterate mode of receiving the Sacrament, with blood supplying for water as the matter, while angels supplied the missing form. He did not see this as an exception to the dogma that the Sacraments are necessary for salvation.