Many years ago, I had a garage fit a new timing belt on my ford Transit campervan. Failure to tighten the front bolt of the crankshaft resulted in allowing the oil pump to 'freewheel' on the shaft, and cause major damage. The garage claimed they had fitted the timing belt without removing this bolt. In actual fact, to do that, they would have had to bend the belt across its width to get it around a rightangle gap of about 3mm. No way could this have been done, but Ford would not rule out the possibility. That was enough for me to be left with the cost the repairs.
If you had got an independent engineer to inspect it and say it was impossible to change the belt without removing the crank bolt then you could have reinforced your claim against them.
Anyway bending a belt the way they described is a 'NO-NO' when it comes to timing belts replacement, So even if they had managed to do it that way they would be guilty of incorrectly fitting and possibly damaging the belt.
Not to mention, Should they have fitted it using the correct procedure then the 'loose crank bolt' would have then be tightened to the correct torque by them during the replacement.