“am I right?”
No
If it is dominant then you only need one bad copy. Father has a bad copy and good copy. Mother has2 good copies. 1/2 of possible offspring will have the bad copy from father and good from mother so they have the condition. Half will have good from both and wont have condition
It could be recessive and she is a carrier so one of their kids inherited a 2-headed gene from each parent
It could be X-linked so father has it and his only son has it (genders of offspring arent noted)
Ditto if it is Y linked (not common, but hey neither is having 2 heads)
Of course spontaneous mutations are possible too. If it is recessive and already have a bad copy from father may have spontaneously mutated the second copy