As has been said many times, if what you are searching for is legal I guess you have little to fear.
It’s probable in this instance that service records from Alpha Computer Service were used, which showed user behaviour and searches on their network.
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Overall, it continues to raise tensions that ISP’s are collecting far too much personally-identifiable data, which may work against individual privacy concerns.
So possibly not all can be levelled at google.
If companies have a suspicion of a criminal activity and take it to the police, yes they are going to use the law to obtain records to support the action.