Shadix, I've been approached by random men lots of times. It is the approach that determines creepiness. I will give you some examples: all of them took place while I was travelling in Turkey.

I had a tour guide invite me home with him while I was in the middle of no where and had not even had a conversation with him. That was creepy.

I had a waiter invite me to play backgammon while I ate. I played two games with him. He invited me to come back to the restaurant that evening for a party. I declined. I did not find him creepy.

I had someone bothering me while I was going about Istanbul. He gave me a weird vibe (forget why it was years ago) so I said I was meeting up with friends. He saw me later that day and called me out on it - which creeped me out. Istanbul is a huge city so that was just not so fun for me!

Had another tour guide when I wasn't in Istanbul (was in a smaller village) who I ran into a lot. Chatted with him a bunch. I was already used to the more blunt approaches taken by men in Turkey, (I stood out a lot being a single female traveller... And I'm very pale). So I totally missed that he was interested in more than just casual friendship (he used to live in Australia so I was less on guard due to his friend-approach. I went on a dirt bike tour just him and I. I clued in while on that.... He invited me to stay the night with him - I declined as I was taking a night bus that evening to go to Istanbul. He tried to convince me to stay anyway, but I declined. If his timing was better I might not have turned him down. I did not find him creepy (or I wouldn't have gone on his dirtbike with him!

It's all in how it is approached. You'll notice the men I did not find creepy were interested in conversation, and they did not interact with me randomly.