There is nothing solid on this and it is very grey.
The best put forward in past was never refer to it as work, but online work related activities would be probably OK if they.
a) do not nor can not be done by an Australian, and
b) are ancillary to the reasons for a Visitor Visa grant.
So a person that can work online or does work online, can check in and do some work related stuff - check all is ok or put out some fires. But not come here and spend 8 hrs a day designing T shirts and sending designs back to their employer.
I would think an Australian could do that task you linked to, without reading it I assume it uses many Independent Contractors.
I think this still applies:
"Tourist visa applicants wishing to work online (for example, wanting to check emails online) should be considered on a case by case basis. If the applicant is holidaying in Australia for a short period, and just wishes to keep on top of work back home (that is, the online work is incidental to their trip), this is not of concern in terms of condition 8101. An applicant who wishes to continue to work online, basically full-time may be of concern in terms of the genuine visitor requirement and should be considered carefully."
It would certainly put the genuineness of a being a " Visitor" in doubt.
I would also be a bit hesitant doing anything with company like the one you mention, If all she stood to lose is a bit of time then it's not a big deal , but certainly dont pay any registration fees etc.
For a company promoting that they teach English, you would think they would have had a bit more professional website!