Trust me, this is not true. Initiating contact is not only acceptable, but quite often preferred. Generally this approach is just protecting your self-esteem.
No, it's a sign of respect. In these days of Tinder, girls are used to guys hitting on them all the time. By not contacting them, you are actually sending a message.
It's quite possible to communicate romantic interest in a way that wouldn't make the other person uncomfortable or suggest disrespect.
Speaking as a woman, the message I would get from this is, "I'm not that interested."