I have never heard the claim before that a sonotube reduces the chance of frost heave due to its smooth surface. The normal explanation for frost heave is water BELOW the foundation which freezes, and expands, lifting up the foundation. That is why foundations are by code required to be dug below the frost line.
Foundations which are dug below frost line do not heave, yet the soil moisture above the frost line is subject to freezing, so the theory that frozen soil in contact with a concrete footing causes frost heave does not seem to hold water (pardon the pun).
The sonotube manufactures simply claim (correctly) that a sonotube provides a convenient, low cost form for placing concrete, and can be easily stripped later if the concrete is exposed. If you dig a hole in the ground and do not use a sonotube, you may use more concrete than required, since the walls of the hole are almost certainly not going to be perfectly vertical.
When I put in my basketball hoop, I did not use a sonotube, I simply dug a hole and placed concrete. The manufacturer specified the minimum weight of concrete required. For my shed, I did use sonotubes.
A basketball hoop is not a frost critical application, unlike a foundation. If you do use a sonotube, and want to avoid frost, you still need to get the bottom of the tube below the frost line, don't count on that slippery cardboard to stop frost heave from below.