NTSB Prelim Details Austin Overflight Incident - AVweb

The following question is asked out of interest, I am not an ATPL and I am not qualified to criticise anyone:

SWA chose to ignore the call to abort, though they had not reached V1.

In general, should a departing a/c abort (if safe to do so) based on a call from another flight crew? For example, a landing crew might see something on a departing a/c that its pilots and ATC could not- such as an engine fire.