Correct me if i get anything wrong here, but this has always been my interpretation of events.
1. Hair calls Murali for throwing. Murali gets biomechanical tests done and clears his name. He had no doosra at the time.
2. Emerson calls Murali for throwing, he gets tested again and cleared again.
3. Some time later, someone (i forget who) calls his doosra into question and when this delivery is tested, it's found to break the laws of the game. Murali is instructed not to bowl the doosra again as it broke the current rules (no straightening of the arm by more than 5 degrees).
4. Tests are carried out on 50-odd other anonymous international bowlers and it's found that they all break the rules, except Ramnaresh Sarwan. To avoid having to test and ban the vast majority of international bowlers, the ICC decided that 5 degrees (and 10 for quicks) is an unreasonable limit and increase the limit to 15 degrees. Hence, Murali can bowl the doosra again.
The reason i don't think there's any foul play involved is that cricket authorities are notoriously conservative, especially with regards to the chucking question. A lot of them, i'd say, don't like his action, and only ended up letting him bowl because the subsequent research left them with little other option (other than to ban everyone). The other theory, that he "fakes" testing, i don't agree with. If he can bowl perfectly legally in a brace, why would he chuck without one?