No, that's not the case. You can always sponsor a dependent and have the application processed outside Canada in the office responsible for their country of citizenship. Even if they are inside Canada.
If legally admitted to Canada for a year or more, the application can optionally be processed in Buffalo (even if the sponsored person is not a US citizen) but you always have the choice of having it processed in the visa office responsible for the country of citizenship.
What actually happened with your sponsorship application. Why did they refuse it (what did they write in the letter)?
Hello Mathew. The application was not refused yet. It was sent to CIC-Mississauga on June 23rd.
23rd July - CIC Mississauga acknowledge the receipt and congratulate me for meeting all sponsorship requirements. They further advise that they will further the application on to Buffalo.
26th July - CIC Mississauga issue revised correspondence which supersedes correspondence of 23rd July - in it they mention as follows:
"This office only processes sponsorship applications for permanent resident applicants that will be finalized by visa offices abroad. Therefore, as a courtesy, we have redirected your documentation to the CPC in Vegreville, Alberta. Immigration officials from that office will contact you in writing as appropriate with respect to this submission."
I called CIC yesterday as I had not heard anything back since that letter. There the call center employee informed that 99% CPC Alberta will reject and send the application back to me (same as what was mentioned by Martha). Due to delay in processing times they have not gotten around to my application hence I have not heard from them yet.
He said that this application must be submitted on H&C ground (again same as Martha) along with covering letter explaining that my child was issued TRP to travel to Canada.
I hope this is clear.