Palm Beach police repeatedly lied and covered for Zac Brown, who was caught up in a drug bust ... and they were so starstruck some of them even asked for the country singer's autograph. As we reported, Zac was in a Four Seasons hotel room a week ago at around 2:30 AM when cops raided the place and arrested 4 people for marijuana and coke possession, including 2 strippers. After learning Zac was in the room but not arrested, we made multiple contacts with the Palm Beach PD brass, all of whom strongly and repeatedly told us they had no evidence Zac was in the room.