Where else does this occur?
Event facilities (for weddings, etc.) often have established partners for various event services that you pay directly rather than through the facility, which you also rent.
Dance studios where the dance instructor is affiliated but not an employee of the studio (especially where the affiliation is non-exclusive) will sometimes (especially for private lessons rather than group classes) charge a floor fee which you will pay to the studio, while the instructor is paid directly.
Fairs, etc., often charge you a gate fee, while you pay for goods and services inside to vendors directly (which vendors are also paying the fair for the privilege of being there, too.)
Arguably, residential real estate leases without included utilities is a closer analogy than any of those: there are a number of non-optional service providers you pay separately, on top of paying the landlord to occupy the premises.
BUT STILL, weddings are a really bad example here.
The people getting married get to chose from whom they want the table and chair covers, flowers, singer/band, catering, belly dancers/entertainment, lights people, AV people.
Those are choices you got to make and the bills will obviously come separate since there is clear distinction of entities. Heck, the venue and the singers might not even of said a word to each other, let alone have a billing agreement.
Well, yeah, that's true by the definition of “subcontractor”, which doctors in hospitals often are not.
OTOH, healthcare isn't the only place where you might pay a fee to a facility for use of the facility and a fee to a service providers associated with the facility for services they provide in the facility. It's perhaps an inconvenient arrangement, but by no means unique.