Ive heard a lot about reharminzation however i am kinda confused now because it appears as though you can basically reharmonize any note with a chord as long as the chord fits that note. Which i wouldnt think would be the case because doing such a thing spontaneously could cause a massive wreak beacuse there is so much more room for error
A reharmonization is typically done in advance and is often written out on the page, so that all musicians have access to it. The song is reharmonized relative to the original chords of the song. So all band members are on the same page, and they don't play clashing scales, etc.
Sometimes, a soloist will "go outside" and play notes that are not part of the written chords. In these cases, the soloist might clash with the rest of the band--and this is often the point. However, advanced rhythm section players will often hear the soloist going out, identify the new chords/scales/changes that the soloist is using, and adjust what they're playing to match the soloist.
Or, the rhythm section players might hear that the soloist is "going out," and they might start comping in a more amorphous way so that they are less likely to clash with the soloist. For example, when a bassist hears that the soloist is "going out," it's pretty common for the bassist to switch from playing the chords and instead play a pedal (stay on the same bass note while the chord changes pass by). A pianist or guitarist might respond by playing quartal voicings (chord voicings where the notes are separated by fourths). Much of traditional harmony is based on the interval of a third, and by playing quartal voicings, the chord often matches a wider range of scales. These techniques can minimize the extent of the clashing.
By the way, your understanding of how reharmonizations work is correct. Your description (take a melody note and reharmonize it using a different chord that contains the selected melody note) is one of the broader, less constrictive ways to approach reharmonization. There are other ways: one might reharmonize only by back-cycling dominants, or only by introducting descending chromatic ii-V's, or by only using tritone substitutions. These and other more constrictive approaches to reharmonizing exist.
When a soloist improvises over a chord sequence, everybody else knows exactly where they are in the chart. It's one person chaanging one thing. The opposite doesn't happen! We cannot have oe soloist playing a melody, and several others playing different chords (from each other) under it. Well, we can, it's called cacophony!
However - any piece can be, and probably has been, re-harmonised. It needs writing down, or at least agreeing upon - so it happens prior to being played, cetainly not spontaneously - unless of course, there's only one accompanying player, and the soloist doesn't stray from the original tune.
It's probably the most used way - as you say - to take melody notes and play a different chord containing those notes. That can get very restrictive, and might involve several changes per bar to accomodate certain notes in a harmonious way. But, there is often no need to incorporate each and every note into a new chord.