They didn't hand over everything. The first thing the prosecution gave him, days after it had been requested, were these psychic "sightings" and "tips" to police where they should look for Caylee.
If I remember correctly, the prosecution didn't want Baez to have this info at first as it was an "ongoing investigation". It wasn't until Baez won the motion in court that the prosecution had to release the info. By what Baez was arguing that particular day in court, anyone with any intelligence can see that he wanted the actual sightings.
What was released to Baez had to already been sifted through as psychic sightings, "tips" to LE on where to find Caylee, and the actual sightings. The prosecution choose to send him the psychic sightings and the "tips" to LE. And it's obvious that the prosecution choose to send him everything but the actual sightings. And now they cry, well it takes alot of time...blah blah blah. While Judge Strickland can't really come out and accuse the prosecution of that in court....I'm sure Strickland is no fool and sees the games that are being played by the prosecution. JMO