All the evidence pointed to Oswald. Then and now. He worked in the building from which the shots were fired. His rifle was found there. Bullet casings from his rifle were found by the window from which the shots were fired. He had no credible alibi for the moment at which the shots were fired. He could not explain the presence of his rifle at the crime scene but instead lied about his ownership of it. He fled the scene within minutes and murdered a DPD officer in broad daylight in front of numerous witnesses. He resisted arrest and assaulted another police officer. He was a known political nut. But it was a "rush to judgement"? HA HA HA. Comedy gold.
It seems the claim is that because at that early stage they hadn't fully looked into a possible conspiracy - and it's true, they hadn't; the FBI among others was still investigating matters, e.g., Mexico City - then Oswald shouldn't have been charged with the murder of JFK?
But that's silly (surprise): Even after charging Oswald that Saturday night they continued to investigate the crime. This was the murder of the president not the murder of a 7/11 clerk. Again, as we know the FBI, the CIA, the SS were continuing to investigate matters, to determine if he had help. Indicting him didn't end the entire investigation. They simply had sufficient evidence by Saturday night to charge him with the murder of JFK. What did they need to wait for? Whether someone else helped him? Or what exactly?
Even if they found later a conspiracy they could charge his accomplices and Oswald as well with conspiracy and other crimes.