From my old RAF days the briefing was something like:
"call all malfunctions with enough info for the captain to make a decision. Anyone may call abort for an engine fire, overheat or failure indicated by 2 parameters. The pilot flying may also abort for blocked runway or loss of control"
or something like that.
Philosophy was that if you were good enough to be operating crew you were good enough to call abort.
I've called abort a couple of times from the FE seat. Once at low speed and once quite high.
It was the FE's job to call the speeds on the Nimrod too.
The removal of this responsibility was the hardest thing to learn once I left the RAF after so many years of being able to call abort.