BBC staff caught watching TV without a TV liscense are subject to instant dismissal. Been the case for eons that company rule and that seems perfectly fair. But that is clear cut and defined upfront in the employment contract. This as you highlight is subjective and no clearly defined lines and that as you say is the job of the police. Indeed this action by them does open them up to the police being involved against them.
If anything, this opens up many opportunities of abuse from nefarious and mischief inclined people.
Lesson to take from this is, don't do personal stuff upon work computers period. That should be the take away message about this type of issue. Remember many an employment contract prohibit that and it is often overlooked if not abused, this may just become that abuse nail example you encounter with HR. Let alone the security aspects for you and your employer, your cloud drive getting a malware payload not impossible and vice versa.