When the Enterprise is approaching the sun they intend to study, Picard announces they will be running with full deflectors up. Surely he meant shields as deflectors are used to clear matter whilst the ship is in motion?
Worf says that the freighter has entered the "planet's" atmosphere. They are orbiting a star, not a planet. However, the distress signal was coming from the 4th planet of the star system, not the star itself.
The Enterprise was originally sent to this system to study its sun. After the rescue mission they should have gone back to complete their mission yet Picard just decided to leave without considering their next mission. The ship does not belong to its captain and the captain would not be allowed to fly around at random. He would have a list of missions to complete which would have been set up, perhaps years in advance, by Federation Command.