Having used DMA in a small number of experimental configurations, and found the documentation "lacking".
I think naming this field as "SOURCE" is confusing.
DMA transfers are triggered by some event, which can include a ALWAYS trigger.
The SOURCE is the source of the TRIGGER.
For some reason the PIT timer gets a special feature in that the TRIG selects the PIT timer overflow as the trigger, but with limitations that you can only use DMA0 with PIT0, DMA1 with PIT1, etc.
While some of the trigger "sources" are obvious, there are a few which I couldn't figure out from the reference manual.