So I guess that you can't really decipher what Mike is claiming beyond his vague allusions to phase correction and kitchen exhaust fans?

I think Mike wants to illustrate with the fan that if you apply a filter to DC the only influence of the phase (to the equally DC) output is its sign.

OK I take up the gauntlet ... that far that I give an "translation" for humans of relevant parts of the first section. I don't think it is worth the time spent. I do and can not say much about the relevance for the sound.

"filter in closed form": closed form means, you can get "the result" explicit and in simple form from the things you know. I.e. you do not need to numericaly solve a equation to compute "the result", "the result" is not given as recursion, or implicit (i.e. as let x be the solution of x^2-2x+1=0), with a more rigor interpretation there are no integrals, summations,....

In the context with filters I have seen that you want to be able to compute the coefficients of the filter in closed form (as function of your design criteria such as passband,...). Usually the coefficients of IIR filters of higher order are hard to give in closed form. Closed form or not is as such nothing that has something to do with the quality of the filter. Perhaps it helps to see what the influence of your criteria are for the coefficients.

"preserves all of the original samples". One thing a filter does is, if you upsample, to fill the gaps in between the original samples. In general it also alters the original samples.

A FIR filter that has, with x-times oversampling, this property would need to have that, for some fixed number k, the filter coefficients with index x*i+k are all zero but one which is 1. An example, you do 2x upsampling and the new sample is the mean of the one left and right. The filter that does that has coefficients (1, 0.5, 0, 0.5). You have the subsequence (1,0) that corresponds to preserving the original samples.

Non of the filter we had up to now has that property, as far as I see (except NOS and Bypass).

"The filter is also time domain optimized which means the phase info in the original samples are averaged in the time domain".

I think, they want to say that they do not only look at the frequency response of the filter but also at the phase while optimizing. The phase of the filtered upsampled signals should be to some extend similar to the one of the original signal (averaging). I.e. the phase response of the filter should be smooth and not to much away from linear (i.e. to much bent).

"for minimum phase shift as a function of frequency from DC to the percentage of Nyqvist - in our case .968." As "we know" preserving the phase is only important for low frequencies. So the phase optimization needs only to be a design criterion for up certain percentage of Nyqvist.

Here the interpretation of .968 not really clear. As "we know" that preserving the phase is only important for low frequencies, taking it as .968% of Nyqvist (220Hz for 44.1) would make sense. On the other hand why then not say 1%. If he means .968 as a factor, so 96.8% that's a lot more than probably makes sense for the phase but fits with the end of the first section.

OK now we come tho the kitchen fan: "Time domain is well defined at DC - the playback device behaves as a window fan at DC - it either blows (in phase) or sucks (out)."

The filter output of a (co)sine wave is a (co)sine wave of same frequency but possibly other magnitude and phase shift.

In the case of DC f=0 the output thus also DC. As the magnitude is by definition positive, the only effect of the phase behavior of the filter is the sign change.