I don't think Virgin or BA really worry about SJ. That is purely because SJ aren't really a threat to them. They operate on one Transatlantic route, Virgin and BA have many other Transatlantic routes.
The reason for fares falling on the Atlantic is because of excess capacity (admittedly which SJ have contributed to) and of course the advent of Openskies in a weeks time. As for low tickets on the Dubai route? Well, that is more likely down to the fact that Emirates are so dominant.
Don't kid yourself that VS or BA are hiding from SJ. They couldn't give a stuff about them. Both BA and VS have more than enough troubles of their own. However, they have the benefit of cross subsidy from profitable routes and far, far deeper pockets than SJ will EVER have.
I look forward to seeing the share price rally on the back of the big investor, but I am still sceptical that SJ will make money before the crunch comes. The whole economic world has changed since last summer. It is a VERY tough place to do any kind of business. Let alone airline business.