Your profile page says you're offline right now (Friday 12:45 afternoon here in Europe).
That being said, I confirm I've noticed the green/grey dots behaving erratically. For example, it sometimes happens that my dot on the Friends list indicates that I'm offline (grey colour), while at the same time it would indicate on my profile page that I'm available for play (green colour). Even reloading the profile page multiple times does not help in such a situation.