Thank you for your helpful replies.
I know the Mighty Rick Steves is not perfect, and I don't expect him or his advice to be infallible. But as an avid user of his books, website and videos, I know that when he makes a point to advocate for one method or another, there is usually a reason for it. Even when there are exceptions, I can usually understand the reason for the "rule," and decide confidently for myself, armed with the knowledge. This one, however, seems to just be incorrect. Having spot-checked with different airlines, third-party sites and times of the year, I just don't see the price advantage I understood him to espouse.
Convenience advantage? Yes. Variety? Check. The moral advantage of not buying through a quasi-oppressive consolidator service? Sure, I see that. But price? Not seeing the truth of it.
I am glad for the warnings about customer service and travel glitches being more-smoothly resolved when booking directly. That, I totally get (although I am mindful that it is not an absolute saving grace, either). And anyone with an eye on Paris would be a fool to think that a labor strike can't pop up and complicate a trip, no matter how careful the buyer is personally.
But I have been lucky, I guess. I have booked two trips thru third-party sites, and I am careful to have all my ducks in a row and my backside at the airport on-time with a simple carry-on bag, ready to go.
When the difference in price is nearly half the overall cost of a trip, it means the difference between going this year, going next year, or maybe not at all. I guess I'll have to mark this advice as just plain incorrect, which is very unusual for one of the most conscientious and knowledgeable (but still-human) travel entities out there.
I will keep an eye out for more posts on this topic, in the hopes of resolving this apparent disconnect. Thanks again to all.