I don't understand this. Trusting which family?

Basically, I don't think there's any basis for your speculation. As has been stated in other threads regarding this subject, this was part of Vito's slippin'. Probably even the grandkids of the five families' Dons knew of Luca's legendary loyalty to Vito. So, there's no way that Sollozzo was going to believe that Luca was dissatisfied with the Corleones. Even if Sollozzo did believe that, he couldn't take a chance that he was right. He had to dispose of Luca - it was an offer he couldn't refuse.