Well, at a pretty fundamental level that's what tonal solfege does - teach the relationships of all notes to "do", which is the exactly same thing as saying "learning how each of the 12 pitches relate to a key". No difference there.
That's not quite right. What he's saying is that when you learn intervals, you learn intervals. You're not really learning them in relation to "do" you're just learning them in relation to the first note that's been played. You learn the interval, but you don't fully learn to hear it in context.
So if you hear two notes three semitones apart you go "that's a minor third!" but you still don't know if it's a 3rd and a 5th or a 2nd and a 4th or a 6th and the octave. (assuming a major key)
What are the songs everyone is taught when learning solfege? The 4th is Here Come the Bride or Auld Lang Syne or Amazing Grace.
Except those aren't root-fourth relationships, those are fifth-octave relationships. But everyone learned it as the 4th because they were focused on the interval & not the key.
It's a fairly common complaint against solfege the way it's normally taught.
You always use "do mi" for a third - but why never fa-la or so-ti? Solfege assumes "a third is a third" - that all thirds are the same, but they're not. Not in the context of a tonal harmony.
So his method (presumably) is to teach you to recognize the difference between "do mi" and "fa la" and "so ti."