Schiff doesn’t say this explicitly but the implication is that flat design is so constricting that the only possible outcome is homogeneity in application design. Certainly, the era of flat design makes it really easy to be lazy. You can make a ‘flat’ app with very little work that gels with modern appearance expectations and looks good, relying on copious whitespace and large typography.
I hate how this has transpired. It is true that the current ecosystem inlcudes a lot of apps that look similar. The important distinction is that it doesn’t have to be this way. The flat world is not constricting. You can make a wide variety of visual styles and colour schemes work. In the skeuomorphic world, it was incredibly easy to create a distinct visual style — just pick a different texture. It’s harder to do original refreshing aesthetics in a flat world (because the tendency to use white is so great) but it is possible. Developers need to work harder to achieve it.
If you want hard examples, the first place to look is the system apps themselves. I think Apple does a pretty good job about offering diverse user experiences in its own apps. Camera uses yellow and black reels, Messages has chat callouts with vivid gradients, Game Center has weird bubbly things and Weather has a vast array of rich backgrounds. Apple isn’t perfect by any means — apps like Videos and Phone are quite lacking in differentiation.
One of the biggest offenders for blandness post-iOS 7 is apps that are basically white scrolling timelines with navigation bars where the only real self-expression comes through a single tint color for interactive elements. In a past life, developers could employ an arsenal of ornamentation (shadowing, gradients) to make these kind of apps stand out.