I have no dog in this fight, merely trying to comprehend. The following statements are copied verbatim from the link:
Improving Stability
"Caution must be exercised when designing a bow with recurve, because bows with greater recurve can also be less stable unless the proper provisions are made to improve the stability. The stability of a bow is its ability to minimize errors induced by the archer upon release of the string, and still have the arrow assume its desired trajectory. This quality is known in the target archery community as “forgiveness”. Since the string must move around the fingers upon
release, the predominant error is inconsistent side-to-side movement of the string while the arrow is still attached to the string.
The ability to resist the side-to-side motion of the string (and thus the perturbations caused by release errors) is often associated with the torsional stiffness of the bow; however this resistance is also strongly associated with the shape of the bow. In a bow with no recurve, such as a long bow, all parts of the bow are oriented toward the archer when moving along the limbs from the center of the bow to the tip. As the bow is drawn, a top view of a long bow in Figure 12 shows that the draw force tends to return the bow to its original in-line orientation when that orientation is perturbed slightly to one side. Upon release, the bow limbs drag the mass of the arrow (through the string) such that the return force tends to rotate the bow to its in-line orientation when that orientation is deformed slightly to one side, as would be induced by a release error. This behavior makes the long bow inherently stable at all draw length."
If the author's view is correct and I haven't seen anyone dispute it, then it's not inconceivable to me that reflex in a long bow limb would function similarly to the tip radius of a recurve limb, albeit on a much smaller and less exaggerated scale . I didn't take it that the author was implying these features to be unequivocally unstable, merely that the tendency existed if the bowyer didn't account for increased torsional stability if his design. I merely point this out as it may answer the OP's original question...where did the reputation come from?