Taqiya by Sunni Muslims

A discussion about taqiya on IraqPundit reminded me of an article I read recently in the NYT:

'There is a notion in Islamic thought called taqiya, in which believers can conceal their faith in the face of persecution. Hamid’s family, Sunnis in the predominantly Shiite neighborhood of New Baghdad, engaged in their own.

As sectarian killings intensified in 2005 and Shiite militias stepped up attacks, they hung two posters of Shiite saints near the apartment’s windows, shattered in car bombings and patched with cardboard. To strangers, they changed their tribal name from Izzawi to Mujahadi, hoping to blend in. They learned not to say, “Salaam aleikum” — peace be upon you — in farewell, as more devout Sunnis will do.'

It's a sad story that reminds us that Sunnis too had to engage in taqiya. But what does the author mean 'they learned not to say "Salaam aleikum", as more devout Sunnis will do'? Salam aleikum, as opposed to "aleikum al salam" (upon you be peace)? I've been saying both all my life, and I'm not devout nor Sunni.