Not true. At the end of the hairs growing cycle, the follicle separates from the skin and waits for something to tug it out. Usually this is either washing or brushing the hair.
People suffering from thinning hair and hair shedding often assume it is linked to washing and brushing and reduce the frequency of washing /brushing. This reduction can paradoxically appear to increase shedding as you can actually save up to a few days of normal hair shedding (50 – 100 hairs per day on average). My advice is to continue washing and brushing 2 – 3 times a week.