Wow, I'd be questioning the structural integrity of the tyre or alignment - was it both front and back?. A well constructed tyre should not allow collapsing of the centre of the tyre at 32PSI.
For example race tyres are far better constructed than street as we know and these are Dunlops suggested ideal pressures in race tyres:
Inflation Pressure Guide:
Sports/GT/Touring = 23PSI
The reason race tyres run low pressures is to allow the tyre to "work" a little with the surface and the sidewalls are far far stiffer as is the carcass. I found all this out the hard way years ago when competing in track sprints in a WRX. I was running R spec Dunlops with 36PSI at the track and couldn't understand why they were no grippier than the road tyres. Tyre Tech advised to try 28PSI and waddya know - tyres warmed up and became tacky

Note I'm not suggesting this for road tyres - merely a point that stonger carcass tyres wont need the pressure a weaker tyre does
Agree we are talking street here, so a rule of thumb from BF Goodrich engineers for street tyres is (weight in lbs/100)
Liberties are 3400lbs? somewhere - makes 34PSI.
Regardless as previously stated there will always be personal preference to pressures run.