Blood vessels become more flexible [1] and there is increased circulation to the extremities. During a sauna, blood flow to the skin increases to as high as 50-70% of cardiac output (compared to the standard 5-10%). This is due to the blood vessels in the skin's surface expanding to accommodate the increased blood flow, a process known as vasodilation. This increased blood flow brings important nutrients to subcutaneous and surface tissue, promoting cellular activity and growth.
There is no citation for that comment, so who knows where they got it from.
But if it is true, do you think it would be beneficial to get into a sauna when taking pills for hairloss? If more of the product was going straight to the skin, it sounds like it would be more effective.