There cant be an investigation initiative just because some (unknown) individual released photos - personal or from investigation file makes no difference, since all photos on the scene are eligible to be included in the investigation - for money.
So, a police officer acting in a official capacity collects photos on police time using police resources, and then sells them for personal profit, and you can't see why someone might want to look into that?
An authourised private photographer takes photos that are supposed to be kept available to be included in the investigation file, sells those photos privately to a company that is not covered by Italian jurisdiction - and you cant think why someone might look into whether those photos were ever made known to the police (you can't include photos you don't know about) and whether or not the photo owner had deliberately avoided making them available to be eligible to be included in the investigation file?
An unauthourised photographer gains access to a crime scene without any apparent permission or notification and then sells the copyrights to a company that is out of Italian jurisdiction - and you can't see why someone might want to know how and when this breach of security happened?
The logic that there's no need to investigate the origin of the photo sale because they eventually end up eligible to be included in the investigation file only makes sense if:
a) there's no possibility of professional misconduct in the selling of the photos.
This can be dimissed as a reason not to investigate as you won't know whether it's a private photo or one taken in an official capacity until you investigate.
b) there's no possibilty of the photos being taken for a private collection by a person who was otherwise working in an official capacity, and thus acting on police time using police resources.
This can be dismissed as a reason not to investigate, as you won't know what capacity the person was working in (and thusly if there's any misconduct for personal gain) when they took the photos until you find out who took the photos.
c) there's no possibilty that the photos were not made available to be eligible to be included in the investigation file.
This can be dismissed as a reason not to investigate as you won't know if the photographer avoided making them available until after you find out who they are and whether they were made known to the police before or after selling - if at all. Arguements about eligibility do not count here if the damage/misconduct was done before they were available to be eligible.
In short, there's little reason not to conduct at least a precursory investigation as to how the photos
and copyrights 'co-incidentally' happened to be sold to a major media agency that just happens to be outside of Italian jurisdiction, and which just happens to be in the victims home country, where the victims biological father just happens to have some influence in the national media. In short, you would want to look into why it has the appearance of a direct targetted leak by a party that has interest in motiviating public opinion against one of the suspects, but who knows enough about Italian law to not risk doing it through an Italian agency.
If it walks like a duck, if it quacks like a duck, and one of its feathers was under investigation for being suspected of belonging to a duck, then you would want to know whether of not it is an actual duck.