If you load up a layer in Construct 3, the Properties panel gives you a number of options in each category. Under "Appearance," there is: a "Transparent" check box, the "Background Color" selector, the Opacity selector, the "Force Own Texture" checkbox, and a readout labeled "Uses Own texture," set to either yes or no.
On my trouble layers, "Force Own Texture" is unchecked, and Opacity is at 100%, but "Uses Own Texture" is set to "yes" without any way to modify it. According to the Construct 3 manual page for layers, Uses Own Texture is "a read-only property indicating if the layer renders to an intermediate texture. This has a performance overhead. The Force Own Texture setting enables this, but some other properties also cause the layer to use its own texture...."
It goes on to explain what other settings can cause a layer to use its own texture even when not forced to. My problem is that none of those settings are active on my trouble layers, which is why I'm so confused as to what is causing them to do so anyway.