The AA-RR partnership says they are the only authorized overhaul facility for Trents in N. America... which means DL either could get authorized to support a fleet of 8 RR powered 777s (the rest are GE powered LRs) or contract out that maintenance (as they must do for the GE90 engines as part of the 777 contracts).
So, yes, DL contracts out what the work which they can get others to do cheaper while using DL facilities to bring in revenue through insourcing for work others want them to do - primarily "common engines" like the CFMs and PW2000s and 4000s.
According to DOT data and DL statements, they receive about $500M per year in insourcing revenue compared to a total maintenance bill for their own fleet of about $2B/year which means that DL achieves one of the highest percentage of insourcing revenue to its own maintenance costs of any major airline in the world.