Not sure how this one escaped me, what with Earth in Apollo images being something of a specialist subject and all, apologies if this is no longer any use and for the mild thread necromancy.
Much of the relevant detail has been covered, namely that not only is it an extremely simple task to use any number of astronomy software packages and websites that will display the Earth in its proper configuration (in terms of the landmasses and oceans on view, the placement of the terminator and its position in the lunar sky), but also to check basic facts.
There is an extremely good website discussing the role of Australia's receiving stations in the Apollo mission generally, and Apollo 11 in particular:
https://www.honeysucklecreek.net/msfn_missions/index.html
The owner of the site is a very nice gentleman and is happy to correspond with people who have an interest in the subject. It would not have been difficult for the Aulis writer to have done some fact checking, or the person with whom the OP was having the discussion.
While there is no specific mention of the Earth being photographed on the surface during the Apollo 11 EVA, there is a record of it being photographed during the broadcast. Here is a screenshot from the broadcast of Aldrin taking a couple of photographs by the base of the LM:
The crew also discuss what they are doing as they try to get the photographs (already included in the posts above)
In fairness not all versions of the EVA footage show the full width of the broadcast, [particularly the restored ones), so most people won't have seen that particular view. Most of the youtube videos just show Buzz's shadow until he emerges into view to take the subsequent images of the LM footpads.
The Apollo 11 Earthrise image shown in a previous post was taken approximately 30 minutes earlier, as indicated by the gap between the Earth limb and the Australian coast.
I'm not sure the Stellarium interpretation given above is correct - my own calculations show Australia rotated much more into view by hatch closure, and Fourmilab's Earthview (which is definitely using UTC) of the view from the moon at the time of the surface image shows this:
There were also images taken from inside the LM after the EVA showing Earth, and while they are not perfectly in focus Australia is clearly visible, eg AS11-37-5506
Australia has not only visibly moved, but it has moved in a way that is completely consistent with the mission timeline.
All of the images of Earth show views completely consistent with the historical records and documentation and can be verified by up to 3 different weather satellite images, all of which were publicly available at the time.