[mothered]

He apologizes because it came to a misunderstanding on his side. He also said: "We will state in the requested investigation that you didn't got the package at all".

Excellent, It's good that they've woken up and realized what actually took place.

As per below, that's why I suggested to ask for clarification.

The point Is, you shouldn't be signing a document that does not represent the actual series of events that took place, hence they need to clarify the questions as discussed.

Then he asked me again to sign the PDF and hand it over to them (my signing is legally binding).
In the PDF I have to sign that "Me xx xx, did not got the package at all!".

There's no cause for concern.

If they had reason to believe that what you're saying Is not true and correct, they would've already taken action and not ask to sign the document. As It stands, there's no evidence to decline your claim, nor suggest that you're falsifying Its details.

and the last sentence: "In the course of this we will ask the driver why he left the package unattended under the carport."

Brilliant.

The driver can create as many fanciful stories as he pleases, but It doesn't change the fact that he left the package unattended via his own volition. His note proves It without a shadow of a doubt.