Just a comment that just because a hydrosalpinx is not seen on HSG doesn't mean one is "out of the woods".
For me, I had numerous HSGs and SHGs that were fine and one that only showed a small hesitation before the fluid went through. Then a few years later it became hydrosalpinx. So then I had that one tube removed, and then the next year, on a followup SHG my other tube was hydro so then had another surgery to remove that one.
However as long as you get checked close to the time of your upcoming treatment, it should be ok I would think like the doctor says.