Yes, it sort of destroys it.

First, pigeons and albatrosses are really remarkably good fliers, and gulls and albatrosses operate in some extremely unforgiving conditions; if they’d chosen birds that don’t deal with as much severe weather or extreme speed (people often just don’t appreciate just how well pigeons fly) you might see very different results, since those are exactly the conditions that are likely to require the high failure margins they point out.

On solid-core, it seems pretty unremarkable to me that feathers may have developed over time to optimize weight-strength ratio. With the higher weight to strength ratio in solid core, the ecological payoff for reducing weight and operating near the failure threshold is a lot greater. You rarely if ever see a modern bird feather broken at the rachis, unless they’ve been in some way crushed, which may indicate that this is not a big problem anymore. Developing hollow-core feathers may have partly removed this constraint, and limited the degree to which you can actually compare the failure criteria.

They also may be underestimating the degree to which flying mechanics can vary load. A good chunk of that high loading at the extremes of the sweep can be avoided with a number of small changes, such as having larger wing area (as I’ve generally seen Archaeopteryx illustrated) and a slightly less efficient, but safer, flap, with lower peak accelerations. Again, a trade-off that results in slightly lower performance, but not a lot.

Another important point is that the bending failure of a hollow structure versus a solid one is very different; I’d have to read the paper to see what exactly how they quantified buckling, but solid-core materials approach failure gracefully, rather than suddenly and somewhat unpredictably coming to a catastrophic failure as hollow-core things will. Think of a straw versus, well, pretty much anything else that bends. Most other things aren’t destroyed if they bend slightly into plastic deformation, but a hollow structure almost certainly will be. Solid-core allows you to actually use that region near the buckling force much more safely, which may be yet another reason why the birds they checked with hollow-core feathers are effectively staying well away from it. When you can safely bend, which hollow-core structures are quite bad at, it has major aerodynamic consequences, and should reduces the peak force on the feathers significantly.

Oh, wow, went on a lot longer than I’d intended to. Long story short:
-They probably had solid-core feathers, which is interesting and likely primitive to birds
-This means they were not the most spectacular fliers, but doesn’t tell us much past that
-Behavioral and environmental factors for the test birds weight the comparison toward a relative appearance of weakness for the ancient birds

These birds likely weren’t the equal of some of today’s highest-performance fliers, but you don’t have to be a “poor” flier to fall out of that category.

I didn’t want to change Brontosaurus, nor Pluto’s status either.