Interpretation of optical depth of photon travelling from stellar interior to surface of star

My lecture notes state:

We define the optical depth as:

$$tau_{lambda}=int_0^skappa_{lambda}rho ds$$

In the case of a photon travelling from the stellar interior to the
surface, $s = 0$ at the starting point, and $tau_{lambda} = 0$ at
the surface of the star. Thus, we can think of the optical depth as
the number of mean free paths for the photon, from a given location in
the star’s interior to the surface.

Earlier it is also said that $kappa_{lambda}rho$ can be thought as the fraction of photons scattered off from a photon beam.

Surely, if the photon which the notes are talking about are at least a bit scattered, than $kappa_lambdarho > 0$, so $tau_lambda>0$. Lets say the notes mean that photon is not scattered at all, travels straight to the surface, ie $kappa_lambdarho$ is $0$. The number of mean free paths is $1$ (not $0$, as $tau_lambda$ is claimed to be there). So how am I supposed to interpret this sentence about optical depth being the number of mean free paths for the photon?