In my experience, there is a difference between the performance sounding bad because of musician skill, and the ear-bending horror of bad intonation.
When I was in college, we played in a touring jazz band with some of the most capable musicians I'd ever played with. The pianist was particularly good. We toured with minimal gear, definitely not a grand piano.
At one hotel ballroom gig, they had setup a stage with a one of the 10+ Steinway pianos from the hotel's many ballrooms. From the 1st register to the 4th register - the piano was badly out of tune by more than a full 2 notes. It was horrible when we played. In that situation - even the piano player continued to play the piano (because that's what our hotel hosts expected of us). I remember begging them to switch the piano for another one just 2 rooms down the hall. They refused. Coincidentally, it was the breaking point of my membership in that group - but that's a whole other story.
With just poor musician skill - the instrument sound may still be pleasing, by chance. Only the other musicians in the audience will probably notice the missed beats, notes, etc.
With just poor intonation/setup - even the non-musicians in the audience will hear that "something just doesn't sound quite right" and perhaps blame a pretty good musician for a really poor sound.
If you are getting paid for a gig - you have no excuse but to at least own a tuner.
Don't rely on the piano!