I think what the OP is saying is that her grandmother remembers/suspects that a man other than the OP's great-grandfather, was her (the grandmother's) father. Whereas everyone else is "oh, yes; he's biologically your great-grandfather!".
@Crockof, you could try a DNA test (Ancestry have the biggest database) and see if other members of your great-grandfather's family - descent from siblings or cousins, perhaps - share your DNA. I think that's going to be the only way you'll definitively find out for certain.
My DNA linked up to solve a family mystery concerning my own maternal biological grandfather. My mother had grown up with a step-father (who was the best grandfather I could ever have hoped for), but knew that he was not her biological father. Her mother refused to acknowledge the fact that my grandfather had only been in my mother's life from the time she was 6 years old - but my mother's aunt and I had our suspicions as to the man who fathered her (she's very like him facially). It was only last year, though, that I worked up the courage to do the DNA test (my grandfather and the man suspected of being my biological grandfather had been dead for about 20 years by this point) and found that my great-aunt and I were right. Luckily for us, my biological grandfather was a lovely man who remained in our lives right up until his death, and knowing conclusively that he was her actual father closed a door for my mother. He was married with 3 young children at the time of my mother's birth - so I can understand why my grandmother wanted to keep it quiet.
Also, DNA conclusively found my step-grandfather's oldest sister. He and my grandmother's father were first cousins, so centimorgans of our DNA are the same. And one of my 3rd cousins was the grandson of a woman who was fostered out at birth as the oldest illegitimate child of my step-grandfather's mother (my grandmother's grandmother's youngest sister). We connected through Ancestry and my 3rd cousin says how healing its been for him to know one way or the other that she would have had a loving family of 7 younger siblings, cousins, aunts, uncles and a grandfather... had the foster family simply not absconded with her.
So, if you can, gather as many memories as you can of your grandmother's early life - and why she suspects that the man who helped raise her was not her biological father... and take a DNA test. Then try to link it to your "tree", through the data which you'll have access to.
Good luck - and like @Saker, I'm more than willing to help if you get stuck.