I'm not sure I buy it. Los Angeles is the second largest MSA in the country and AA can't make long haul flights work there except to partner hubs, even when they were the largest carrier in LAX. DL has AKL, CDG, HND, LHR, SYD, and seasonally PPT out of LAX, but UA manages to fly from LAX to secondary markets in Australia, even before their VA partnership. They are also going to be the only US carrier that resumes LAX-PVG.
If you look at a list of CSAs ordered by population and note which airlines have hubs there, you get:
NYC: AA (ish), B6, DL, UA
LAX: AA, DL, UA
WAS: AA (domestic), UA
CHI: AA (ish), UA
SFO: UA, AS
BOS: B6, DL
DFW: AA
HOU: UA
PHL: AA
ATL: DL
MIA/FLL: AA
DET: DL
PHX: AA
SEA: DL, AS
MCO:
MSP: DL
DEN: UA
CLE:
PDX:
STL:
CLT: AA
SLC: DL
SMF:
PIT:
SAT:
I'll give you that UA has strong hubs in the top 5 markets, but that doesn't really explain why they are able to make things like EWR-OPO, EWR-PMI, SFO-AMS, SFO-FCO, IAD-AMM, ORD-SNN, or LAX-BNE work when AA/DL can't. That also doesn't account for UA's significant return to PVG from ORD/LAX/EWR/SFO, with plans to return to PEK from SFO and ORD in the fall.