After researching this issue for over a week, I finally found a workaround that may help some. When I talked to the customer service rep, she said that because I could access AppleTV on all my Apple devices, she couldn't help me any further. I decided to see if I could download the AppleTV app on my laptop (not an Apple product). I typed in "tv.apple.com" on my search engine and the AppleTV website came up. I entered my password and I was able to access all of the programming.
My Samsung TV is supposed to be able to mirror an iPhone but it wasn't working. As a result, I just took an HDMI cord, plugged one end into the TV and the other end into my laptop and I was able to watch AppleTV on my big screen. Not as easy as simply gaining access to my third party options from my Smart TV but at least I won't have to watch AppleTV on my iPhone.
Hope this solution helps someone out there who may be experiencing the same problem.