Acetic acid is a mild chelator, far weaker than EDTA. Nevertheless, you can demonstrate for yourself the chelation process in action using the organic acid in vinegar (acetic acid).
Take an eggshell and place this in a bowl with some vinegar. Over a period of several days the eggshell will become increasingly thin, as the acetic acid progressively chelates the calcium out of the shell. Add more vinegar and the shell will eventually have all of its calcium removed, leaving it in solution, bound (chelated) to the acetic acid.
It is just this process, much more efficiently performed, that EDTA achieves in the body when it acts on unwanted calcium deposits which are obstructing normal function.
Remember that EDTA only does this with ionic, unbound, calcium and thus will not leach calcium out of the normal bound sites such as the bones and teeth. By removing ionic, free calcium from the bloodstream, EDTA triggers parathyroid hormone to be released, which in turn compels the body to unbind metastatic calcium which may be cementing atheromatous plaque deposits in the blood vessels. In this way circulatory normality is encouraged.