It's also worth noting that these letters cost about 1000 Euros each, there is almost nothing you can do about them, and they require not the slightest bit of evidence that you actually did anything wrong.
"In cases involving peer-to-peer sharing of music files, the value of the claim was regularly set at €10,000 per file by the rights-holders...Recipients of Abmahnungen often pay the costs without consulting a lawyer, or negotiate a settlement themselves. There is a noticeable tendency to pay rather than challenge the claim..."
and
"the evidence collected about the infringement will only identify the IP...This IP address needs to be matched against the subscriber to whom it was allocated at the time of the infringement...by way of a judicial disclosure order...[in which] German courts are rather reluctant to engage in an assessment...[for instance] within 9 months in 2009, 2824 disclosure orders were sought in Cologne alone, each relating to several hundreds of IP addresses."
[1]-The RedTube copyright infringement affair in Germany: shame on who? (http://www.tandfonline.com/doi/full/10.1080/13600869.2015.10...)