  Strongly correlated topological surface states are promising platforms for
next-generation quantum applications, but they remain elusive in real
materials. The correlated Kondo insulator SmB$_6$ is one of the most promising
candidates, with theoretically predicted heavy Dirac surface states supported
by transport and scanning tunneling microscopy (STM) experiments. However, a
puzzling discrepancy appears between STM and angle-resolved photoemission
(ARPES) experiments on SmB$_6$. Although ARPES detects spin-textured surface
states, their velocity is an order of magnitude higher than expected, while the
Dirac point -- the hallmark of any topological system -- can only be inferred
deep within the bulk valence band. A significant challenge is that SmB$_6$
lacks a natural cleavage plane, resulting in ordered surface domains limited to
10s of nanometers. Here we use STM to show that surface band bending can shift
energy features by 10s of meV between domains. Starting from our STM spectra,
we simulate the full spectral function as an average over multiple domains with
different surface potentials. Our simulation shows excellent agreement with
ARPES data, and thus resolves the apparent discrepancy between large-area
measurements that average over multiple band-shifted domains and
atomically-resolved measurements within a single domain.
