You're saying the same thing in different words. "Warmer" in sales means "more influence on the recipient to agree".
Up-thread they said they explicitly asked for email instead after taking the cold-call. What's the good faith reason for insisting on a warm phone call when it's not wanted?
In almost 100% of the cases, if a Recruiter is able to get someone a job, it's immensely beneficial to the new employee, far more so than for the recruiter.