No there is no evidence that i have seen that he is a british agent. But this idea of what truth is has guidelines, and as you said it has different guidelines in an islamic court vs when you don't have access to one. Which will leave us left with our own witts.
If a group of people have a good track record according to most decent people(now we could discuss what and who is decent) then of course there would be more room for benefit of the doubt than towards a group that has been involved in fishy activities for over a decade.
In case of Habib, it's the same thing, without being 100% certain, i'm naturally inclined to believe Nasrallah over Habib due to their trackrecord and not their turbans or its colors, which is also direcrly and indirectly recommended by our faith to do. Trusting the words of someone who is regarded as aadil by more than many fellow shia muslims + a pretty impressive CV is nothing short of a logical approach un my opinion. Politics might play a role yes, but track record outwheighs it by far. And many shias do not seperate politics from religion as you know, so this idea would just regarded as: "Religion plays a role".