Energy conservation is an essential feature of optical waves propagating through refractive turbulence. It has been known for almost a quarter of a century that energy conservation has an important implication for the fluctuations in the images of the incoherent objects observed through turbulence, namely the image of the uniformly radiating area of an object does not scintillate. As a consequence, the low-contrast parts of an image exhibit weak fluctuation even for very strong turbulence, but scintillations near the sharp edges can be strong even for weak turbulence. The energy conservation property of the turbulent point spread function is essential for modeling turbulent image distortions, both for the development of the image processing techniques and for simulations of turbulent imaging. However, it is regularly overlooked in discussions of turbulent imaging theory and modeling in the current literature. We discuss the relations between energy conservation and anisoplanatism for the most common turbulence imaging models. Our analysis reveals that the only isoplanatic turbulent point spread function (PSF) that is compliant with energy conservation is the thin aperture plane phase screen. This implies that for near-the-ground imaging, and even for astronomical-type imaging under strong turbulence conditions, the turbulent PSF has to be modeled as a random function of four arguments with three functional constraints: non-negative values, finite bandwidth, and energy conservation.