No, you are correct to wonder. Infertility is a long process to determine. Both partners are tested & if the man has had a vasectomy, it's usually reversed, if possible, before IVF attempted. It is extremely rare for a woman to get pregnant on their 1st try.
When my husband & I first got married (second marriage for both of us), we looked into IVF to have a child together. I had had my tubes cut & cauterized years prior & my surgery could not be reversed. The only way for us to have a child was for my eggs to be surgically harvested, fertilized in the test tube, & implanted into my womb. Because I was 46 at the time, I would have had to undergo hormone treatments & there was a very big possibility that it would take more than 1 attempt. Plus I ran a high risk of giving birth to a handicapped child due to my age. Once we found out everything we would go through, the expense & no guarantee we would be successful, we decided not to go through with it. We already had 3 sons between the two of us.
IVF is a long, involved process so I'm not buying her infertility BS. Jim had vasectomy but had frozen some of his semen prior to his surgery. Apparently, they didn't even check to see if his vasectomy could be reversed. She's not infertile. They just took the easy way & thawed out his sperm & she got pregnant right off. Her infertility claims are complete BS & are just so she can have a story line.