In a decades-old system, the FAA lets engineers employed by manufacturers themselves oversee tests and vouch for safety
That's not an entirely accurate representation of the delegation system. The people who "vouch for safety" are actually making a "finding of compliance" (FoC) to the prevailing design requirement. The FoC may be made by an FAA staff member, or a person delegated by the FAA, who might be a manufacturer's employee, or an independent person, contracted as needed. A delegated person (who is not an FAA staff member) exercises that delegation (to make an FoC) on behalf of the FAA, and values that delegation, as a privilege which could be lost, if abused. On the surface of it, like a pilot, a delegated person making an FoC toward the approval of an aircraft during certification, should be regarded as dedicated to aviation safety. It must be understood, that for projects as advanced as modern airliner certification, the US taxpayer could not afford to have the FAA employ enough people to entirely understand the complex systems and software of the aircraft - delegation is necessary to see the project to certification. The FAA may have whatever involvement they wish in a certification project. The FAA is duty bound to oversee enough to have a broad understanding of the whole project, and a detailed oversight of novel or unusual aircraft systems being certified.
Under the new rules, which took effect in 2009, the agency let Boeing pick the employees who would vouch for its safety. Previously, the company only nominated them.
The nuance here is pretty important - "pick" vs "nominate". Ultimately, no matter how the person is presented to the FAA, it is the FAA who appoints them as an FAA delegate. If the FAA is not satisfied that that person will act objectively with public safety, and a design compliant aircraft as their priority, delegation would not be appropriate.