There's an important difference that you're missing, in that the DMCA was passed in to law, and it completely changed the situation.
Before the DMCA the parties met in court as equals, and a judge (or jury) had to rule as to whether the claim of infringement was valid. Because this required effort to prove, and because courts really hate having their time wasted, this tended to prevent baseless claims from being made. And until the claim was proved to be valid, the site was unaffected.
The DMCA completely shifted the balance in favor of any claim of infringement. All claims of infringement are presumed to be valid, and that the ISP/Site must immediately take down anything claimed to be infringing (the "safe harbor"). And then, after the site is down, the burden is on the site to prove that the content is not infringing.
So looking at the Qualcomm / Github situation, before DMCA Qualcomm would have filed claims in court and Github would make the case against the claims, and the claims would have to be proven, with the repository owners able to defend themselves from the claims, before any repositories were taken down. That is, the burden of proof is on the person claiming infringement, and nothing happens until they make a case in court. And if the claims are baseless, all that happens is that Qualcomm wastes a bunch of money, and pisses off the court, and likely has to pay Github's expenses.
Under DMCA, Qualcomm files claims, Github has to immediately take the repositories down, and then each repo owner has to prove that their repo is not infringing to bring it back up. So Qualcomm has, without any proof at all, forced tons of repositories down, and even if they've done nothing wrong it could be months until they're back up, damaging those projects and wasting huge amounts of their time and money.
Those aren't the same.