Can an hsg test be 100% correct at diagnosing a patient with closed/blocked tubes?

Pretty close to it: The HSG test is done by inserting either a small catheter or a cannula into the cervix opening. You then inject contrast (xray dye) while watching on the xray fluoroscopy. You can see the contrast fill the uterine cavity and tubes. Sometimes the HSG will push out little tube plugs and open them but it will (if done properly) see if the tube is open or blocked.

Not 100%: No, it's not 100% accurate, but it's pretty good. There might be tubal spasms preventing the dye from passing through the tube. I believe you just had surgery, and it can take 2-3 months for healing to be complete. This might effect the results. If the HSG shows blocked tubes 3 months after your surgery, that would be concerning. A laparoscopy could be performed and a dye test done.