While theoretically true, I think for most accounts the risk is fairly small: I'm sure it's hard to come up with something to tweet from my account that moves any stock exchange even a penny.
I think if you really try even your account could move a stock. Think about it: A tweet with location (in front of a big company's CEO's house) early in the morning when you know the 'target' is commuting, flying or otherwise offline, followed by a tweet 'just killed the bastard' with a fake photoshopped picture of a body'. If someone was to target a person with a love of guns on their timeline... well things could get messy real quick.
There was some contention about that last year with the NetFlix CEO releasing subscriber numbers on Twitter that affected the stock, but the SEC issued guidance earlier this year that said that disclosure on Twitter and Facebook were ok, as long as the accounts were public.