The advice to book directly is repeated constantly and is only sometimes correct. The real difference is who holds the contract, and that matters mainly during disruption.
The contract determines who can act
A booking made through an intermediary creates a contract with that intermediary, which then holds the reservation on the traveller's behalf.
Changes, cancellations and refunds must pass through that party, and the supplier will frequently decline to act on a reservation it does not control.
During a disruption that adds a step at exactly the moment speed matters, particularly when the intermediary operates in a different time zone.
Suppliers protect their own bookings first
When a hotel is oversold or a flight is cancelled, the party making the reallocation decisions is the supplier.
Guests and passengers whose bookings are visible directly, particularly those with loyalty numbers attached, are generally handled ahead of opaque third-party reservations.
This is not a stated policy so much as a practical consequence of the supplier's incentives and of what its staff can see on the screen.
Direct rates carry conditions of their own
Direct booking often includes benefits such as loyalty accrual, free cancellation windows or small inclusions that do not appear on intermediary rates.
It also frequently comes with the cheapest non-refundable options, which are a poor choice for a trip with any uncertainty regardless of where they are bought.
The comparison worth making is between equivalent conditions rather than between headline prices, since the flexible direct rate and the cheap opaque rate are different products.
Intermediaries do things suppliers cannot
Combining flights from carriers with no commercial relationship is only possible through an agency, and for many itineraries there is no direct equivalent.
Package arrangements in several jurisdictions carry statutory protection covering insolvency and repatriation that a set of separately booked components does not.
A capable agent also absorbs the work of a complex rebooking, which is worth a great deal on a multi-sector itinerary that has broken.
A workable rule
Simple bookings on one supplier are usually best made directly, since there is nothing to combine and the contract stays clean.
Complex multi-supplier itineraries and packaged holidays benefit from an intermediary, provided it is one with real support rather than only a booking engine.
In every case the question worth asking before paying is who will answer the phone if the trip breaks, and whether they can change anything when they do.