Sud,
Each C6670 corepack has a dedicated AET and ETB units. So if before you attempted to run the trace example on core 1, you used CCS to setup a core trace trigger on core 1 but not core 0, you will only see the claim error when you try to run the example on core 1 and not core 0. If you did not have a core trace trigger setup from CCS, let me know the revision of the libraries you are using (ETBLib, AETLib, DSPTraceLib) and I will try to reproduce the issue.
Yes, it is possible to use EDMA to transfer ETB date to memory. ETBLib has support built-in to dma trace data to memory. See the example project at Examples\C667x\DSPTrace_TIETB_EDMA_Ex_CorePacN.
Regards,
Doug