Getting back to he original question: where is the authority to close a river?
The link that lead to the AW posting is somewhat misleading. The statute it references 33-13-111 authorizes the Board of Outdoor Parks and Recreation to promulgate rules for the closure of waters to vessels, but also specifically excludes whotewater canoes and kayaks from the definition of vessels in that section.
There is therefore the argument that nobody has the authority from the legislature to close a river to whitewater canoes and kayaks.
However, the statute gives authority to any Peace Officer to enforce the Board's policies with regard to anything other than a a kayak or canoe, i.e. a raft and possibly even a ducky.
Violation is a class 2 petty offense with only a $100.00 fine as a penalty. No jail, no probation, no arrest (summons only).
A class 2 petty offense should only get you a summons, but keep in mind that being a complete D-bag to a sheriff's deputy could get you arrested on some other BS charge (resisiting, obstrucing, trespassing) and get you hauled off to jail to wait for the next bond hearing on monday. That can be a long weekend of wondering where your boat and your gear are.
Please keep in mind that I am not your attorney.