I find this quite an interesting tidbit of information, because there is nothing on the 1040 to indicate your immigration status. The only way the IRS can determine that is to run your SSN through E-verify.
So what this clearly means is that the reason why some non-immigrant visa holders are getting cheques and why others are not is because of errors in the SSA database.
If you got an SSN before they got E-verify up and running and are filing a 1040, most likely you got a stimulus check. If you got your SSN later on then most likely you didn't.
It's all down to what the clerk typed into the SSA computer when you got your SSN.
If you have since changed status to LPR and have never informed the SSA, what you need to do is go down to the social security office and get them to amend your status in E-verify to remove the restrictions on your work authorization. Then the IRS will be able to see that and you can get your stimulus check, assuming the SSA can backdate it, which I doubt they can, but you have the basis to appeal the refusal in their system, at least.
You should frankly do this anyway, I'm not sure on why the SSA are so coy on telling people about it. When I phoned them up when I was in the US it took a long while for that bit of info to come out in the conversation.
http://www.canuckabroad.com/forums/some ... t2611.html
Steve.