She did have massive legal backing - that "junior" minister to whom you refer is the highest official for sport in South Africa and while his influence with the IAAF will be limited, there were very powerful political forces here in South Africa that fought the battle.
Legally, she was represented by the same law firm who represented Oscar Pistorius - they became famous, incidentally, because when South Africa's government changed, they were one of the firms that handled our Truth And Reconciliation hearings. Kind of like the Hague in SA. So it's fair to say that globally, they're one of the big firms - offices in NY, and here.
Just on the note of medical testing, UKAthleticscoach is quite right - the testing and diagnosis of conditions is not difficult. 20 minutes is all it takes to establish if someone has a uterus or not (of course, if the person has internal testes, they don't have a uterus). Another few hours and you have a very clear picture of what has happened biologically. A couple of days for genetic test results, a couple more for hormonal.
All in all, you know exactly what biological condition you're dealing with in a week or two. It's not that complex.
What is complex is deciding what to do with this information. You could decide that the biological differences do NOT confer a performance advantage, or that they do. this is the essence of the debate, i guess. But the 11-month delay is NOT due to medical guys sorting out the issues medically, that was the PR and legal spin.
The only reason for that delay could be:
a) There was a legal arm-wrestle which saw Semenya's lawyers pulling out the rights issue and compelling the IAAF to allow her to run on the grounds that they could not find evidence to ban her (this is much what Pistorius succeeded at doing). Or
b) The IAAF have worked with Semenya to supervise and administer medical treatment in an attempt to reduce the testosterone levels and thus the advantage. The medical experts thus being referred to would be guys who are evaluating how her hormone levels are changing with the treatment (oestrogen and knocking out testosterone production).