Slightly expanding the topic, but here it goes....
The key in the liner insulation issue is that nothing ever meets code unless you follow the instructions - doesn't matter what part of the stove system you are talking about, you only meet code if you follow the instructions. If you don't meet the stove clearances to walls and mantels that are combustible, then you have a non-compliant install.
Your liner has clearances too - they are in the instructions. Sometimes, they say nothing more than "install in a code compliant chimney", and sometimes they do a better job and spell it out. Even better, sometimes they tell you what the clearances are with and without insulation.
In the end, you have to follow the instructions - don't follow the instructions, then you won't meet code, and you may have a latent safety hazard on your hands that rears it's ugly head in 5, 10, 15 years.
Not sure why some folks go nuts over an inch on a hearth extension, and spend extra time and effort on getting the R value they need for the floor around the stove, and then choose to ignore the clearances for the liner. But many do, and it seems illogical to me.
I actually had a certified installer in my house yesterday who was willing to admit that not installing an insulated liner when we know that the chimney doesn't have the clearances was a clear code violation. When I asked him if he would start insulating them, he said in 15 years he has only done 2, and doesn't plan on starting now.
I hold the same sentiment for folks who want to shove various insulation types around liners as block off plates - they wouldn't think of not meeting clearances around the stove, but then they shove fibreglass up the flue to keep hot air from passing around the liner - using that stuff around a liner is not in anyone's instructions, and is a bad idea.
So, in the end, buy a liner that comes with good instructions, and follow them. If they say to insulate, then do what they say. Don't do what your buddy says, unless it is the same as what the instructions say.
But, once you insulate the liner, you don't need clearances around the brick, so you can wrap it in whatever you want then.