When isSAGBI is supplied a SAGBIBasis or a subring, there are two generating sets which can be used: either the generators of a subring or the subalgebra generators of a SAGBIBasis (which may be stored in the cache of a subring).
If the flag is set to false, then the check is applied to the subalgebra generators of $SB$. If the flag is set to true, then the check is applied to the generators of the subring of $SB$.
The object UseSubringGens is a symbol.