Is it true walking bare foot is not good if you have high arches?

No, not exactly: If you have high arches and you walk without any symptoms of discomfort, then there's nothing to be concerned. However, if you are having pain and/or developing severe thickening (calluses) on the ball and heel of your foot, there are some abnormal pressures created by having high arches and you may want to follow-up with a podiatrist to see your options.

It depends on factor: Anything in moderation is fine however high arched feet may be more prone to problems with increased activity its always a good rule to start slowly on a soft surface, but in the long run a good pair of shoes and an orhtoses may be helpful as well.