Functional Scala programming pattern matching

Studying the Functional Programming book by Manning and struggling a bit. Doesn't the below hasSubsequence fail because the first time it encounters the first startsWith(sup, sub) returning false the whole function hasSubSequence returns false at that point and it does not check the subsequent letters?

@annotation.tailrec
def startsWith[A](l: List[A], prefix: List[A]): Boolean = (l,prefix) match {
 case (_,Nil) => true
 case (Cons(h,t),Cons(h2,t2)) if h == h2 => startsWith(t, t2)
 case _ => false
}

@annotation.tailrec
def hasSubsequence[A](sup: List[A], sub: List[A]): Boolean = sup match {
 case Nil => sub == Nil
 case _ => startsWith(sup, sub)
 case Cons(h,t) => hasSubsequence(t, sub)
}