hmm, I think you are answering yourself here, The Quran does not deny event of crucifixion did not happen, it is saying people think they are hurting Jesus but in reality, it is someone else
Historically we know Jews were persecuted by Romans when they accepted Christianity why because they thought Jews conspired to have him put on a cross
Quran says they think - it could mean Jews or Romans or both - we know Jews alone cannot have crucified him because they were not in power, they could have influenced or pressurized Romans
Jews were waiting for a Messiah like David who would make them rule, but Jesus despite calling him Messiah did not show those qualities but claimed to be Jews Prophet - It is possible elders of Jews did not like it and considered him an outsider trying to take over their religion
for e.g, there is a trick question they posed to him, so if he had said do not pay to Cesar, they would have him convicted in court for that
Another one , they tried to tick him , if he would have said stone the adultery , they would have used that case against Jesus since it will go against Roman law
Jesus was a wise man, he used his wisdom to get out of both situations and did not break the mosaic law and Roman law.