Even the American Fertility society, the group most IVF doctors belong to has said that reversal is a cost effective alternative for women who have their tubes tied if they are under 42 years of age*. This is true and it’s a lot safer and more likely to give you a baby. This is a group of doctors that do IVF! For most forms of female-related infertility other than having your tubes tied IVF can be your only option, but not for women who have tubal ligation. If you were not fertile, you never would have had your tubes tied in the first place.
My best guess as to why your doctor told you that IVF was your only option is that the drugs that are used in IVF are very expensive and they have an extensive publicity campaign to promote IVF. Every year that company goes to most cities and invites Ob-Gyn doctors to a free meal at a nice restaurant to hear a talk over dinner and drinks about these expensive drugs. They come every year, here, to Gainesville , Ga.
*Ferility and Sterility July 2015 Vol 104 No 1