I've been in touch with the municipality and the local historical society and was grateful to receive a very detailed reply from the latter.
In short, the statement on the municipal website is not correct: the most likely origin of the naming of the hamlet as 'Anzac' was by returning Canadian soldiers who had fought alongside Australians & NZs on the Western Front and after demob, worked on the railway in the post-WW1 period. Up until post WW1, the hamlet was known as Willow Lake - it was only renamed once the railway arrived circa 1921.
There were certainly no 'ANZAC' units working in the far reaches of Alberta, Canada (or anywhere else in Canada) during the First World War, as is indicated by the statement on the municipal website.
The historical society will be approaching the municipality to have the website statement amended.
As an aside, there is also a locality called Anzac on the Parsnip River in the back blocks of British Columbia. So both places are probably named to commemorate ANZAC troops, but for their efforts on the Western Front rather than in Canada. An interesting little aspect of history - thanks, Peter for posting the link.
Mike