Support group for 5 years - assessing me income?

I migtated from Incapacity benefit 5 years ago onto ESA into the support group. I have been kept in this at my last assessment in 2017.
today I received a letter stating I am receiving contributions based esa and I need to fill in a form to see if I am eligible for incomes based esa. as far as I can find out if you are in support group of contributions based esa then this is not means tested. I am obviously going to be on the phone to them first thing tomorrow morning but we all know what fun that is!
Am I right in my thinking that support group esa is not means tested?

All sorted it was nothing to do with my esa as it is now in support group but was told by a nice but fed up call handler that between 2011 and 2015 thousands of people who transitioned from incapcity benefit to esa were not assessed to see if they were eligible for income based esa and if they were they could have been eligible for other benefits and this is what the letter was about just totally uselessly worded as usual! I just had to say if I would have been eligible at anytime between 2013 and now and if so they would have worked out how much money i was owed. As it is I have never been eligible for income based esa so thats it. Once he had explained what had happened it all made sense and he said they had not been shown a copy fo the letter that is being sent out. He said that they were inundated with people in a total panic like me who were worrying that they had suddenly started means testing the support group. He was alot more cheerful when I had thanked him for explaining so well.