According to the GDPR: "If data is in any way identifiable, or can be connected to the user (directly or indirectly), the data collection process cannot make the claim of being anonymous".
That is why we only claim the analysis to be anonymous, because obviously there is a way to connect the personal data with the response data if someone maliciously wants to do so.
However, there are many solutions that claim "technical anonyous data collection", but there are often ways to get around this.
Especially with smaller data samples it is especially dangerous. Open ended questions are also a danger zone, because depending on the answers you can often know who the person is that answers. Or if you ask people from smaller groups within the sample.
So now you know that there are 2 people in a specific department. One of them gives a low rating for the office temperature and as HR manager you already know that Mrs X is always complaining about the office being too cold, while Mrs Y has previously been very happy with the office temperature. From now on you can be basically 99% sure that those answers come from Mrs X, rather than Mrs Y.
Or you send the invitation out in batches. Let's say batch 1 is sent at 1pm and batch 2 is sent at 5pm. Now you know, that all responses between 1pm and 5pm are from batch 1. Depending on the batch size, answers, etc. you can make a lot of assumptions and "de-anonymize" data that seems to be anonymous.
I just wanted to say that even processes that claim total anonymity can be misused, if there is maliscous intention. Therefore anonymity is also always connected to trust. If you take the definition that you posted very literal, I am sure many, many solutions that claim to collect data anonymously are lying. Because with a little bit of effort, often you can find ways to connect response data with a specific person.
But you are totally right: in the case that I described in my previous post, we can't (and don't) claim that the data can not be connected, we can just promise that the personal data will never be connected with the response data, even if we could.