[bilky asko]

To be specific, in what way would the BBC trying to "catch people out" by listing the Australian series 5 and 6 as 1 and 2 respectively?

The BBC are the only ones referring to the two most recent seasons as series 1 and 2.

I believe they're the only broadcaster outside of Australia and New Zealand to show the series, so I'm not sure what the relevance of that is.

I can see why they would do that - to make the show more appealing to viewers because it isn't seen as "old", and in the case of "series 2", people are more likely to want to catch up if they think there is only one previous series, so the re-numbering drives use of the iPlayer. The situation also reflects more positively on the BBC, them being seen to being fully committed to shows as opposed to buying in selected episodes. Ultimately, no questions are asked if people see "series 1" and "series 2".

Despite the conspiratorial tone, that still doesn't explain how it is supposed to "catch people out".

The more reasonable explanation is that they have bought the rights to show the revived series on the strength of Lord Sugar's presence. Because the chances of them showing the previous series is precisely zero, they have numbered it accordingly.