Sinaloa, Chapo, Mayo, Vicente, never had immunity from the DEA, they definitely paid off high level government officials, (Mexican) but it was never as simple as immunity, or bribing a president. There was a lawyer, named Humberto Castro Loya, who had permission from his boss, Chapo, (who represented the interests of El Azul, Mayo and Chapo) to cooperate with US authorities, to inform on rivals and weaken their organization. This lawyer gave info to DEA about Juarez Cartel, Beltran Leyva brothers, after the separation in 2008, and what was left of the CAF in Tijuana post 2008.
Now, the lawyer, and Vicente Zambada got a little carried away, and Vicentillo wanted a meeting in Mexico City in 2009, at the Sheraton. Vicente basically wanted the same deal for himself, to cooperate with US authorities. Maybe his father wanted it too. These guys often misunderstand how US law enforcement works. DEA, had been trying to get Vicente since the Flores Twins cooperated, the previous year, they set up the meeting, no showed, rearranged the meeting, and then arrested Vicente directly afterward, using Mexican federal police, or I think the Army. Then he was extradited.
The whole "I had immunity" was just legal strategy from his lawyers. If they had immunity the DEA would not have used the Flores Twins to basically build a case on Chapo, Mayo, and his son. There is a lot of rumors and gossip and lies in the narco world, it's hard to keep it all straight.