no- it is not true- back in the (old days) dyes were acid dyes-and vinegar set them- now days pretty much only wools are still dyed with acid dyes-
the dyes that are used on cottons are not acid dyes-
the vinegar will soften/freshen your fabrics but will do nothing for (retaining/setting) colors.
visit Dharma Trading Post- they have free information sheets & tutorials that will explain/teach you pretty much anything you need to know about dyeing fabrics/setting colors/making batiks/fabric painting---they also carry all of the supplies needed for the various techniques.