Hello,
I'm not saying they did it, but it's easy for the for that company to create a fake email now that looks like it was sent back in August.
The only information you can trust will be data from servers that you trust.
Did your mail server see a connection from the IP address of the server in Switzerland on August 12th?
Do you trust the owner of the mail server in Switzerland? If so, you can ask them for related mail logs from that day.
Since they claim they sent an email, but also claim that they know it failed, either way they are claiming they know whatever email you expected was not sent and/or did not reach you?
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