Hm, The link to the Springer (Manchester) article isn't working this morning. Points to the journal but not the article.
Meanwhile the Newcastle article has references to other articles doing similar things: "Data collected from Mumsnet have previously been used to describe the views of parents (particularly mothers) and answer a wide range of research questions [17-20]."
which led me (among others) to this from UCL (2020) https://mental.jmir.org/2020/9/e18271
"The use of mumsnet by parents of young people with mental health needs: qualitative investigation. JMIR Ment Health."
MumsNet might possibly have agreed to this one but there's no indication that MNHQ were asked or permission was granted, and it looks as if the reverse is true:
"Parsehub was used to extract data from Mumsnet threads. Parsehub is a freely available web-based scraping tool designed to extract internet data. Any original posts or comments including information that could potentially identify the user, such as age, name, or location, were omitted manually by the researchers before the data were analyzed. Following this, the raw data were transferred into word documents for analysis."
So this team UCL have been scraping conversations between distressed mothers about their children with mental health needs. The paper includes brief anonymised quotes from individual posters.
And to start answering @MarkMenziesFakeMugger why do they think this is OK?
The ethics section says they had approval from the UCL ethics team, plus this:
"In line with the recommendations of the Association of Internet Researchers Ethics Working Committee [23], all data were extracted without the inclusion of usernames, and direct quotes were altered slightly (without changing meaning) to maintain the privacy of those posting on the forum during the initial data extraction stage of the analysis."
So here is a link to that paper about ethics: https://aoir.org/reports/ethics2.pdf
Markham A, Buchanan E. Ethical Decision-Making and Internet Research: Recommendations from the AoIR Ethics Working Committee (Version 2.0). Association of Internet Researchers. 2012.
Members of the AoIR Ethics Working Committee who contributed to the report are listed at the top, dunno what the mix is of Information Retrieval and ethicists. It's rather elderly (2012) My quick skim and a keyword search says that this document does mentions copyright as a potential problem, and terms and conditions. It mentions scraping right at the start but nowhere else. It says this is ethically complex and it doesn't mention the bleeding obvious - try reading the Ts&Cs and asking the site owners. Maybe they have a better idea of what's acceptable on their own site than you do!