Trump may not be able to overturn an Obama or previous designation by himself, but having Zinke review them and then seeing if Congress wants to "alter or rescind monument designations," as they did in Alaska and in Montana certainly is within his authority.  
 
"Legally Bulletproof"  is hyperbole by the R-G editors, not the law.  

The Supreme Court cases were mining and water rights interests who wanted to overturn a Presidential designation; not one President overturning or modifying a previous President's designation.

That case has never been litigated.  

If he can cancel a US Treaty with another country just by notifying Congress, I don't think this kind of designation is absolutely "Legally Bulletproof"!