This implies that some agencies apply on behalf of the applicants.
Another possibility is that agencies make unsolicited offers to recruit a candidate on the institution’s behalf.
While I don’t think that universities are likely to make use of such a service, I can expect that such offers can be annoying and even rejecting them wastes a considerable amount of time.
Also, the recruiting process is not limited to applications.
There may be agencies who make enquiries because they think that the job may be a good fit for a client – though it clearly isn’t and the client would never apply.
I am regularly contacted by recruiting agencies (and even companies) who could have seen with a short glance at my CV that I do not match their job offer at all.
In some cases, this process was at least semi-automatised as I received the same offer twice via different channels.
It thus wouldn’t surprise me at all if such agencies blindly offer their services to anybody posting a job ad (matching some automatisable criteria) on certain sites.
Of course, it is debatable if agencies that do not even notice that a job offer is academic will notice the warning in question, but adding the warning in question to a university’s general boilerplate costs almost nothing.
[…] do open positions without the above statement accept applications sent by agencies rather than the applicant?
I strongly doubt this; they just haven’t annoyed by recruiters to the extent that they created this boilerplate warning.
Note that in my (admittedly limited) experience, the existence of such a warning depends on the country.
I have never seen such a warning for positions in Germany, but almost every job ad from the Netherlands and Belgium had one.
This may be due to different attitudes towards and of said agencies in those countries.