I'll have to say I have NO experience with the HD opener, but have had several newer vehicles that have the Home Link on them.
I have Chamberlain door openers, but one new one with wifi that I bought through Sears and one original one. Both came with the little remotes etc.
But the newer Home Links will NOT pair up with the older Chamberlain opener and I've had to just clip the remote on the visor and live with it.
I know Yellowcorvette fixed his issue as it was a faulty assembly at the factory, but there may be some with the newer CVO's that might still have a pairing issue with the older garage door opener.
My old one says it has the "floating" codes, but after doing tons or research on it, the industry did make some changes in past many years and some fully functioning GDO's still will not pair.
I will say though that my new Sears/Chamberlain with belt drive, battery backup, and phone app, is the bomb. My neighbor texted me after he saw me leaving my house for work one morning and said I forgot to put down the door. I stopped and opened my app on my phone and hit close, done deal...

I've also opened it for my neighbor to access my garage to borrow items. Also just to joke with the neighbors, we had a big storm go through this area a couple years ago that knocked out our power and we were all standing outside watching the clouds, you know, like when there's a tornado warning and everyone runs outside to take a look??? Well I went back in the house and pressed my opener and when it got up I walked out. They all asked how I had power and they didn't. Ah ha, battery backup worked again!
Sorry to digress and those with much more experience than I have supplied the correct information, but just wanted to add that SOME older openers may not pair well with the newer Home Link or HD GDO options.