IIRC the largest ISP in Australia is Vodafone who provide more mobile IP connectivity than anyone else. (Source: Personal discussion with senior management, ~5? years ago)
Whoever told you that was being very liberal with the truth, Vodafone has always been #3 in the Australian mobile market since they started, they were hemorrhaging subscriptions for most of this decade due to underinvestment (known as "Vodafail").
They only started providing wireline services very recently, one of the few "western" markets they were not a full telco player in.
The discussion was around mobile IP connections. I am not sure if your calculation includes for example (just guessing!) other mobile carrier branded services using their network (MNVO[0]), non consumer (eg. IOT type or vehicular) mobile nodes, etc. I would trust this person implicitly as I used to work for them, they are an engineer not a salesperson and they are not known to extend the truth. While no information is infallible and perhaps they were wrong, given their position, however, I doubt it.
I can't see this being true for IoT/M2M either, sorry. There are a couple of small MVNOs on Vodafone but nothing that would bridge the gap between them and the other players.
_Maybe_ they have a good share of multinational contracts from their parent company, that is the only area I can see this statement being true.
Vodafone are doing some work with NB-IoT but the general market for this are metro utility companies - the coverage doesn't exist out of these areas to be taken seriously for a nationwide fleet.
I would put good money on the number of payment card terminals and power meters alone on Telstra being bigger than Vodafone AU's entire M2M business.
As sibling commented, Voda is distant third in Australia. The incumbent is Telstra, with ~50% mobile share and was the dominant fixed provider pre-NBN.
Telstra's mobile footprint is vastly superior to the other two MNOs in terms of geographic coverage.
