A plant controls erosion by binding soil with roots and by breaking the force of rain before it hits bare ground. Both take time, and time is the whole problem.
A new planting on a slope does not hold anything. Root systems that will eventually knit a bank together are, in their first season, a scattering of small plants in loose soil — and the first heavy runoff does not wait for them. That is why a slope planting is two jobs: the plants, and whatever holds the ground until the plants can.
Which one depends on the slope. A gentle grade may need nothing more than mulch and patience. Anything steep wants erosion blanket, matting, or terracing, and on a fall install it wants it before winter rather than in spring.
The plants themselves divide by how they hold. Fibrous, spreading roots knit the surface and stop sheet erosion. Deeper taproots anchor against slumping. A good slope planting usually has some of both, and groundcovers that spread to close the gaps between them.
Honest version: if somebody is told the plants alone will hold a steep bank through a heavy runoff year, they have been told something that is not true.