You can ask for a small sum to train them to produce proper PDFs. If they prepare everything in Photoshop, then they will have a hard time switching to InDesign or Illustrator. As the learning curve will be steep, you will have a lot of phone calls, follow-up online sessions, etc. In the end it can take months to move them to the right track, a great job from a trainer's view, which needs to be honored.
To the original question: I agree with Matt, you should ask for PDF/X-4 files, as they allow a lot of changes, while retaining the original content. But for the most sophisticated alterations, like trapping, filling up missing bleeds, matching colors across jobs, etc. you will need a high-end software like PitStop Extreme, ArtPro or PackZ. Their associated cost is so high that you might be tempted to ask for the native files instead and struggle with them in Illustrator/Photoshop. Don't be frustrated, BIG international companies doing well using only Illustrator CS3 only for package design.