Historically they're correct in that Somali women dress much more conservatively today than they did 100 years ago, however west African style head wraps are not traditionally Somali.
Traditional Somali dress for women was a Dirac dress (or in more isolated areas, clothing made from hides) with her hair tied back with a scarf and a shawl over her head. You can see photographs of women without either scarf or shawl from the 19th century but you can see in the photograph that she is holding her shawl and scarf in her hands, and has just taken them off for the photograph. When working or it's otherwise inconvenient they would take their shawl off but keep a loose scarf, usually dark in colour, over their head to tie back their hair. Photos of women assembling shelters for instance they have taken their shawl off which would get in the way.
In rural areas where Somali women did not have access to the right textiles, they don't wear a scarf or shawl but just tie their hair back with a chord. It was virtually unknown for women to wear veils for instance in the past, that is entirely a modern phenomenon. Women wore brightly colored diracs with elaborate shawls and often had lots of jewelry. Fashion was more elaborate in Mogadishu where the locals were wealthier, whereas in rural areas the most elaborate thing a woman owned might be a dirac and some bracelets or especially necklaces.
19th century photographs show incredibly elaborate necklaces and often lots of piercings for earrings and arms covered in bracelets. Somali fashion for women was very ostentatious with visible demonstrations of wealth and prestige, something that's declined terribly due to the much more conservative era today.
