No I think you're right. Like say the dominant curly gene is "C" and the recessive straight gene is "c" - and each parent carries two hair genes, one from each of THEIR parents. Mom's genes could be CC, Cc, or cc. For the recessive trait to show up (i.e, straight hair) both genes would have to be recessive. So the first two combos would produce curly hair and the last one would be straight. Dad's could also be CC, Cc, or cc. We know since they're both curlies, both parents have to be either CC or Cc. And since their kid is a straightie, we know both parents HAVE to be Cc, and had to have passed on the recessive gene from each parent to their kid. So the kid has cc hair.
That's a really basic example and that being said, I haven't taken biology in 10 years so I could be remembering genetics wrong too
ETA - I have a daughter with straight hair. I know I carry the straight hair gene from somewhere. My mom's hair was curly but my dad's I'm really not sure on, it's been really short my whole life. So I could've gotten it from any number of generations back. My daughter's father has straight hair. It's a less dramatic example as the OP, but I was for sure I'd have little curlies running around when I had kids and while my daughter's had a few spirals as a baby, it's pin straight now as she gets older.