Add checks for improper qualified accesses

Author: avik-pal

test/misc/qa_tests.jl

@@ -26,4 +26,6 @@ end
         skip = (NonlinearSolve, Base, Core, SimpleNonlinearSolve, SciMLBase)) === nothing
 
     @test check_no_stale_explicit_imports(NonlinearSolve) === nothing
+
+    @test check_all_qualified_accesses_via_owners(NonlinearSolve) === nothing
 end