Forensics is a way to do things (procedure) so that you can use your findings in court. It is up to the opponent to challenge certain methods, like "you used md5 hashing which is proven unreliable", or something like that.

"They will use that as evidence supporting a warrant to search a suspect's computer" Indeed, you won't be called to court just because your ip address in on a list. There will be further research which could result in: We found this video on the computer which was downloaded from [source] as shown in the logs from with this ip.