on shaky ground
Questionable or lacking support, as of an idea. His hypothesis has been on shaky ground to since the beginning, so I'm not surprised that he couldn't prove it in the lab.
on shaky ground
and on dangerous groundFig. [of an idea or proposal] on an unstable or questionable foundation; [of an idea or proposal] founded on a risky premise. When you suggest that we are to blame, you are on shaky ground. There is no evidence that we are at fault. The case for relying solely on nuclear energy seems to be on dangerous ground.