Okay, lets clarify some things.
First, a good way of thinking about polyrhythms is that the second number in the ratio is the "unit pulse," or what your body is actually feeling. This would be the "1's" from the pen and paper method that I described in the video. This pulse would be what your foot taps to, and what your head nods to. The first number is "calculated" against the second number, and the represents the rhythm you actually play on your instrument.
Measure 1 in the above example shows a way of understanding 4:3. The bottom stave has 4, evenly spaced notes that take the span of 3 quarter notes. Measure 2 on the other hand, shows what 3:4 would look like. The pulse that you feel is the quarter notes, and the cross rhythm that you play is the 3 evenly spaced notes (felt in triplets). Measures 3 and 4 are other ways of writing the same exact same rhythms show in measures 1 and 2
With me so far? Good, because now I'm going to confuse you. Notice the metronome markers in the above graphic. If you had two bass players performing these rhythms exactly as notated and with the exact metronome markings, all 4 measures would sound EXACTLY the same. What's changing is the unit pulse (what your body feels), but 4:3 can be flipped to sound like 3:4 and vice versa via something called metric modulation. Don't believe me? Try inputting this into a notation software like Sibelius and hear what comes out.
To get an idea of what this sort of shifting of meters and polyrhythms sounds like in context, check out an excerpt from the second movement of my large ensemble opus, Exigence.