It's more subtle than that. What "agile" does (both Scrum and XP, historically) is _protect the delivery team_. With waterfall-style project management, early errors balloon but often don't surface as something that needs addressing until implementation and testing, so the delivery team gets all the stress for blowing out the project schedule.

Agile techniques both surface those errors early, so they're course-corrected quickly, and provide a set of clear rules for the rest of the organisation to abide by which should mean that the delivery team can't get overloaded into a deathmarch.