You're partially right.
The last couple of stories have stated that it is the largest and second largest respectively. Completely wrong there, but it is the third largest by a significant margin (and has been for several years)
There is also a significant margin to the next largest (Optus) but it is still a very definite third. A quick google search proves that.
iiNet also has a large amount of infrastructure. Other comments have mentioned that they were the first to roll out ADSL2 and it certainly wasn't on Telstra equipment. Again, their infrastructure isn't to the scale of Optus and Telstra but they do have substantial presence.
You are also partially right on the last point. They aren't going after Telstra or Optus as they have a lot of resources behind them. iiNet is the perfect candidate to test the waters as they have enough marketshare for a win to actually be significant while not having the overpowering resources of the two largest players.