How are 12 outputs being reconciled so that a Homomorphic filter could be applied?
From my reading, the authors don't combine the 12 images in a single image: each generates a directional scratch mask, each of them being processed independently. If I read too fast, tell me. Indeed, they first remove a low-pass version, and apply a logarithmic homomorphic filter. But you could combine the binary masks with an OR to get a single image of potential scratches.

However, it would be possible with filters alone to recombine them by addition.

Suppose that you only have two filters $f_1$ and $f_2$, that are applied to an image $i$. $\mathcal{F}$ is the Fourier transform: $I=\mathcal{F}(i)$ and $F_k=\mathcal{F}(f_k)$.

The hypothesis that they do not overlap is related to their frequency behavior, with spectra $F_1$ and $F_2$. Their supports $S_{F_1}$ and $S_{F_2}$ (imagine 2D patches in the full 2D frequency domain $S_F$) do not overlap if their intersection is void: $S_{F_1} \cap S_{F_2}= \emptyset$. What is not explicit is that, often, the filters are also complementary, their union covers the whole frequency domain: $S_{F_1} \cup S_{F_2}= S_F$. Thus, the spectrum $I$ of $i$ is cut into two complementary parts, and $I = F_1\cdot I+F_2\cdot I$. Then, you could recover $i$ with
$$i = \mathcal{F}^{-1}(F_1\cdot I+F_2\cdot I) = \mathcal{F}^{-1}(F_1\cdot I)+\mathcal{F}^{-1}(F_2\cdot I)\,.$$

Equivalently, this amount to directly write, in the original domain:

$$i = f_1\star i + f_2\star i\,.$$

Visually, the frequency domain is a pie, and each filter is a slice. When you have the the slices, you can reproduce the original pie. In practice, people don't use exactly non overlapping filters in frequency, but orthogonal filters in space, that sum to unity to equally cover all frequencies.  This is a little more general as non overlapping filters, as $F_1\cdot F_2 = 0$, thus $f_1\star f_2 = \mathcal{F}^{-1}(F_1\cdot F_2) = 0$,  are a subset of orthogonal filters.