This is correct. The C++ standard specifies that sort must have a big-O complexity of n log(n). This can be seen on pdf page 925 of this working draft from 2014 [1].
[1] http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2014/n429...
[1] http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2014/n429...
The standard doesn't seem to say "or better" here, but I know that in other places it does (or least used to say something similar).
Note that this wouldn't be true if the standard said that it has to be Θ(n log n).
If something is O(1) it's also O(n) and O(n!), since it's an upper bound.