There are many singers with absolutely fantastic technique that do not know how to have vibrato on a note. So this idea of “healthy singing” = vibrato makes no sense in the real world of singers unless you’re only looking at it from a classical genre perspective. In that case you’ll likely “catch” vibrato as a result of being immersed in the vocal effect.
There are also many singers with technical problems who also have vibrato. They may have a vibrato that they can’t control, for instance it’s too wide, or too fast for their taste. Maybe they aren’t even intending to have vibrato and want to have some control over it. I wouldn’t tell those singers to tighten their throat in order to get rid of it, so a good technique doesn’t equal vibrato…perhaps a good classical technique.
Vibrato is sliding your voice up and down within the range of a note, like singing an A 440hz, then sliding to an A 445hz, then back down to 440hz, in rapid succession so that the note sounds like it “wavers”. It’s the same thing you do for moving higher and lower in your voice, except the range is very very small.