The second that men must be aroused to have an erection. Both of these myths are wrong, wrong, wrong. You are correct when you say that erections can be caused by anxiety. They also occur for no reason at all. Most often erections are caused by sexual stimulation.
Stimulation is a physical response to a stimulus.
When someone steps on your toe, the stimulation you feel is pain and there is nothing you can do about that. It does not mean that he is aroused. Arousal is a mental and emotional thing. You can be sitting and fantasizing without any outside stimulation and become aroused. It can certainly be caused by seeing or hearing something that turns you on.