I couldn't resist some back of the envelope calculations.
Schwarszchield radius: \[r = \frac{2GM}{c^2}\]
Newton's gravitational acceleration:
\[a = \frac{GM}{r^2}\]
Acceleration at the horizon:
\[a = \frac{GMc^4}{4G^2M^2} = \frac{c^4}{4GM}\]
Just looking at orders of magniture: \(c = 10^8\), \(G-10^{-11}\), \(M = 10^{41}\) gives the approximation \(a=10^2\), which is close enough.