There are four possible combinations between a method of achieving solution, i.e. with TRIZ vs. without TRIZ, and solution's merit, i.e. good solution vs. bad solution. Here is the list of combinations:
Combination 4 is obvious: history of any human endeavor is full of bad solutions, and certainly most of them were achieved without TRIZ.
Combination 3 is obvious too: all good solution achieved before TRIZ were achieved without TRIZ. TRIZ publications are full of such solutions. TRIZ authors retrospectively tailor some of them to fit TRIZ, but it doesn't change the fact that they were achieved without TRIZ. Of course there are millions of good solutions that are not even tailorable.
Combination 2, according to TRIZ, is not possible. Usually, when a bad solution achieved with TRIZ, TRIZ experts would find a mistake in a way TRIZ was applied. Usually, they do it retrospectively, when it becomes clear that the solution is bad, - not unlike the retrospective tailoring for combination 3 above. However, the examples for combination 2 do exist: they are bad solutions found with TRIZ by TRIZ experts themselves. One of such examples can be found here: A Brain for Intelligent Design: A new scientific concept for biological evolution, Boris Zlotin and Alla Zusman, Ideation International, Southfield, Michigan, 1985 -- 2000.
The authors are renowned TRIZ scientists. The article includes detailed explanation, why and how TRIZ was used. The solution is bad, in fact so bad that no professional biologist even bothered to refute it. Thanks to Boris Zlotin and Alla Zusman for providing us with such a clear example for combination 2.
Combination 1 - this one would be the most interesting, but is the most difficult to find.