I remember they were not so clear,actually MG was unrecognizable.Maybe I'm wrong and this is not the case,but it's increasingly difficult to distinguish between professional and amateurish photos. They were outside a shop,it could be that someone recognized him,followed them and took the pics. Michael was photographed on the Slow West set while he was peeing.. those pics were taken by a person working there,for example. It's VERY probable that she called paps in Milan,she lives there.. But even in that case there's a ( minimum) possibility that someone recognized him,there are always paps who hang around in Milan centre.I want to give her the benefit of doubt..
I wasn't necessarily speaking of some incontrovertible evidence

,just a more friendly attitude.In the first pics they were not even alone,when they were lunching she was busy looking at her phone.. It's no coincidence that people are still saying "they are filming together,they are just co-stars,I don't see anything between them!". This is just my opinion,but I think that he doesn't live his life thinking continuously of what people may think.. He likes to fly under the radar but IMO he's a person who doesn't give a damn

if he wants to do something he likes. He likes to surf,he had the opportunity to do what he likes there before leaving (this is not a proper, planned vacation),so he did it. If they will not be seen together again (I doubt it) he's still in the position to say "we are just friends!"
,if they will continue to be seen together,it means that he has no problem dating her publicly.