I don't know very much about family history, but I have a friend that is a regular genealogy wizard. I asked her and this is what she said (you will need to log in to FamilySearch to see the links):
Thanks for giving me a chance to do some genealogical research for fun! I began to answer your question by going to FamilySearch and inputted Mervyn’s name, birth, and death date. I found his FamilySearch profile here (KWZS-CJ3). His parents are Israel Bennion and Jeanette Sharp. I did not see Adam listed as a sibling.
I then searched for Adam S. Bennion and found his FamilySearch profile here (KWJ8-M9D). Adam’s parents are Joseph Bushell Bennion Sr. and Mary Ann Sharp. Mary Ann Sharp is Jeanette’s older sister, so technically Adam and Mervyn are cousins.
I continued my quest to see where President Eyring fit into the mix, and I went to RelativeFinder.org since it’s a super cool website to see which famous people you’re related to. President Eyring is my 10th cousin three times removed in case you were interested. Since FamilySearch doesn’t allow you to see other people’s profiles that are still alive, I went to Mildred Bennion’s (his mother) FamilySearch profile here (KWCV-B2T). I searched her FamilyTree to see if I could find a connection to Adam and Mervyn.
I clicked on the “View Tree” button and did the same with the other two men. I found a common connection between all three of them: John Bennion (KWJB-NG4).
The FamilyTree progresses like this: President Eyring is the son of Mildren Bennion. Mildred is the daughter of Marcus Bennion (KWCJ-KHY). Marcus is the son of John Bennion (L67-VHF). John is the son of John Bennion (JWJB-NG4).
Mervyn Bennion: Mervyn is the son of Israel Bennion (KWCG-N11). Israel is the son of John Bennion (L67-VHF). John is the son of John Bennion (KWJB-NG4).
Then Adam Bennion is the son of Joseph Busnell Bennion Sr. (KKC3-3Q9). Joseph is the son of Samuel Bennion (KWJ8-SR4). Samuel is the son of John Bennion (KWJB-NG4).
If that doesn’t make sense, just look at each of the FamilyTrees and you’ll be able to see the connection as long as you follow the Bennions.
In conclusion, you’re correct! President Eyring is related to both of these men, but they aren’t his direct grandfathers.
There you go! Also, another way to say that they were cousins of his grandfather is that they are his first cousins twice removed.