Validity of an argument that two transfer functions are minimum-phase based on their ratio being minimum-phase
two transfer functions HL and HR can each be represented as a minimum-phase filter (MPF) plus a pure delay.

That is generally not true and it's easy enough to disprove it by counter example. Let's simply look at a first order all pass
$$H(z) = \frac{p-1/z}{1-p/z} = H_{MP}(z) \cdot H_{AP}(z)$$ which has a pole at $p$ and a zero at $1/p$. The &quot;minimum phase&quot; part, $H_{MP}(z)$ is simply unity, i.e. $H_{MP}(z)=1$ and the all pass part is just the original all pass. The all pass phase response is NOT that a of a pure  delay, we clearly have $\Phi_{MP}(\omega) \neq \omega \cdot t_0$
I think you misunderstand the point in the paper: I think they are just saying that a specific class of transfer functions can be approximated well with this model. In this case this class is &quot;HRTF ratios for human heads&quot; and they show that this works particularly well for spherical heads. Since binaural perception is mainly based on interaural differences, approximating the frequency dependent interaural time delay by a single constant value can be quite useful.