It's this blanket statement that private investigations are illegal on PT soil that I don't understand.
I don't think it's quite a blanket statement.
Indeed it can't be, because I seem to recall that, way back, I researched it a little and discovered that there are private investigating agencies based in Portugal, which obviously there wouldn't be if private investigations in Portugal were illegal.
I think it's just that you can't conduct a private investigation in parallel with an official investigation into the same matter.
Possibly, but check my questions further up.
Even if it is in relation to the same matter:
1. what exactly is the difference between a private investigation and well-intentioned citizens, tourists, whatever (possibly in an informal group) trying to help?
2. where is there a definition of a "private investigation" and an article in the penal code relating to it to distinguish it from point 1?
ETA: Yes, I understand your point about "into the same matter", but I still don't understand what is supposed to be illegal per se.