Sorry to say that, No, you can't.
Either you allow all users to view logs or none, there is no per user control applied to this setting unfortunately. The only thing you can control is the channels for which a user can view logs.
I am sorry to say, I see no easy way of solving this. For a standalone version you could create a custom user group that only differs from standard users in regards of viewing logs. But, the problem is that you use a integrated version that I guess relies on user credentials used in the forum. And even if you didn't, it would require some work regarding coding from your end, to create the group and edit the source to allow that custom group to view logs.
So it seems rather hard to achieve I'm afraid.
//FireWire