Patrick was on a security mission at an oil well, and he stayed together with a group of people; not only were they not in Baghdad, but they were also quite far away.
Recruitment couldn't be done openly, since Trifolium Jungle was also a major corporation. Directly going to another company's defense area, then specifically asking to see Patrick, and finally stating the intention to poach him would result in, not just failing to meet the person, but probably getting kicked out directly.
Thus, undermining someone definitely requires a strategy; you need to have tactics.
Gao Guang and his team didn't take the Humvee out because a Humvee mounted with a machine gun would be too conspicuous and dangerous after leaving Baghdad, possibly attracting a hostile RPG.
Furthermore, driving two Humvees bearing the emblem of King's Defense directly to Trifolium Jungle's defense area would certainly not grant them entry.