The 2003 ABC News article Some U.S. Troops Choose Historic Tomahawk doesn't show that US Navy SEALS, in particular, use tomahawks, but shows that their use is somewhat common amongst modern US military, and makes the claim seem more prosaic.
Members of Air Force security groups, Army Rangers and special forces are some of the U.S. troops who have chosen to add tomahawks to their basic gear. [...]
It wasn't until after the Sept. 11, 2001, terror attacks and the United States began fighting in Afghanistan that [a manufacturer] started making [tomahawks] in quantity. In fact, it dramatically changed the way he does business — Johnson says his time is now almost exclusively devoted to producing the modern tomahawks for military customers, and he makes only a few historical tomahawks a month. [...]
Currently, service members are buying tomahawks individually or, in some cases, units are using operational funds to buy them for their group.
The terms "primeval" and "weapons" seems to be a little exaggerated. These are of a modern design, and while they might be used as a weapon, they seem to be carried as a more general tool.