The first paragraph is common stuff....The individual instrument resonates in response to all the frequencies transmitted to the corpus (body) through the bridge. but the amplitude of the frequencies passing into the air and to listeners depends on the amplitude/frequency characteristics of each particular instrument.
The player's vibrato spreads the breadth of the fundamental (fingered) tone's frequency and thus the also of its overtone frequencies. This can activate some higher (and lower) sound peaks depending on the instrument's resonance spectrum, thus creating additional richness, "projection" and apparent loudness of the sound.
Good players will will control their vibrato to (try to) produce the sound they want from the instrument they are playing by adjusting the breadth and speed of vibrato motion. Experienced players trying an unfamiliar instrument may have to adjust their vibrato to the nature of the instrument to get the desired sound from it (if it is possible at all).
The second and third assert something I've wondered about... that the vibrato actually alters the timbre rather than merely being perceived as warmer, richer, etc...