The Empire still wasn't nearly as powerful at the start of Star Wars as it was.... in the middle of it.
Remember, that officer talking to Vader was worried about a PR disaster: "Holding her is dangerous. What if word gets out? It could generate sympathy for the rebellion in the senate."
And even Vader is trying to cover his trail: "Send out a distress signal. And then inform the Senate that all aboard were killed."
Then a few days later, Palpatine dissolves the Senate,...