On a general conflict of interest note, I believe that there cannot possibly a captain who will play his friend or relative, at the expense of the team. Its just some mischief makers who when they disagree with a selection look at things from a conflict angle.
Proximity with the captain if anything makes things more difficult for both the person under scrutiny and the captain.
I will give the example of Shukhar Dhawan from earlier in the year, when he was woefully out of form, but Dhoni kept backing him and backing him, and ultimately Dhawan went on to have a stellar World Cup and was among the top 5 highest run scorers in the tournament.
Now since Dhoni and Dhawan are not relatives and not known to be great friends, it was easier for Dhoni to back Dhawan, as no one could attribute ulterior motives to Dhoni in that regard. Had Dhoni and Dhawan been business partners or great friends or relatives, it would have been far harder for Dhoni to back Dhawan, as people would then have not stopped talking about how Dhoni was looking out for a friend over the team.
Its the same situation with all captains. I find it hard to believe that any captain will put an individual ahead of success and the team. Just that where there is that extra relationship between the captain and the player under pressure who is being backed, it just gives the mischief makers room to have a go.