No problem with the embrace, big problem with guys holding on to me way too long with heavy breathing and or stroking my back in a creepy way. There is a difference between rubbing someone's back in an affectionate way, like when you are talking to a friend, and back stroking in a creepy way. Have had the hands wander in all directions and it wasn't pleasant.
I don't think it's being frigid to want to dance in a nice embrace without the guy assuming that means you are open to being groped or going home with him. If Anna is coming away from her dances feeling that the embrace was sexualised (sorry if that word isn't allowed here)- "I felt like I was cheating", and he was actively doing stuff, I don't think it's a case of a beginner thinking the embrace is an erotic thing by default and dreaming up the cheating aspect.
Maybe I'm a freak but as I danced almost exclusively with men in their 60s when I was starting out as a little 20 something I have never thought of tango as 'sexy'. You can have a surprising and 'intense' dance connecting to the music and each other etc, but really? Am I supposed to have some kind of attraction to all my partners? Come off it, it's just a dance. A Grandad can give you a warm and generous embrace just as well as anyone else and more often than not they don't decide to start pulling at your bra or putting their hand on your arse. Does that mean my lovely grandads are doing it wrong?