The spell can't be countered if the mana produced by Boseiju is spent to cover any cost of the spell, even an additional cost such as a splice cost. This is true even if you pay an additional cost while casting a spell "without paying its mana cost."

Suppose mana produced by Boseiju is spent on a spell and an effect creates a copy of that spell. The copy can be countered, even though the original can't.