TL;DR: the DMCA takedown provisions apply only to third-party service providers identified as a Designated Agent, and can be avoided by self-provisioning online services. Or finding a provider with balls.
The specific mechanism of the DMCA is that:
1. It is a protection afforded online service providers, specifically, against infringement liability. (17 USC 512(c))
2. Against copyright infringement (17 USC 512(c)(1)).
3. For third-party content (17 USC 512(c)(1)).
4. Of which the provider does not have specific knowledge that the content is infringing (17 USC 512(c)(1)(A)(i)). (More on this below.) And does not directly benefit monetarily (17 USC 512(c)(2), and acts to disable access expediciously (17 USC 512(c)(3)).
5. Where the provider has a designated agent. (17 USC 512(c)(2)
6. A valid notification request is received, (17 USC 512(c)(3)
https://www.law.cornell.edu/uscode/text/17/512
A consequence of all of this is that a self-serving online service provider does does not qualify for the relief as the content is not third-party. By designating itself as the Designated Party, it can choose to receive DMCA requests directly, and assume the risks of infringment claims itself.
There is nothing in the DMCA that says a service provider must act on a claim. Only that the liability protections offered apply only if it does. Linode, here, absolutely could have taken the principled stance that the content was not infringing, and refused to act on the notice it had received. Yes, this would incur a liability, but the overall legal risks of a patently false and malicious claim would be slight. I believe there are cases of this occurring.
NB: A longstanding criticism of the DMCA 512 provisions was that there was no liability for misrepresentations. That's now addressed in 17 USC 512(f), though I don't recall when this was added:
Misrepresentations.—Any person who knowingly materially misrepresents under this section— (1)that material or activity is infringing, or (2)that material or activity was removed or disabled by mistake or misidentification,
shall be liable for any damages, including costs and attorneys’ fees, incurred by the alleged infringer, by any copyright owner or copyright owner’s authorized licensee, or by a service provider, who is injured by such misrepresentation, as the result of the service provider relying upon such misrepresentation in removing or disabling access to the material or activity claimed to be infringing, or in replacing the removed material or ceasing to disable access to it.
Mail & Guardian would seem to have some remedy here, if they can successfully bring suit and collect judgement.
It's also possible that M&G could bring suit against Linode under 17 USC 512(g)(1) ("good faith" actions), though that's weakened by subsequent paragraphs. Informed legal opinion would be helpful here.
Note: I am a space alien cat, not a lawyer.