Read and understand this carefully: the project (video) profile that I have selected is correct and it correctly matches what the video is supposed to be! I expect the frame rate to be 29.97 fps, Nautilus properties report the frame rate to be 29.97 fps (it actually just says 30 fps). I've set the frame rate of the profile in Kdenlive to 29.97 fps before importing any clips - so I know that I'm using the right frame rate in the project for the right frame rate of the video.
If I import a clip, the audio is visibly shorter than the video (there is a period of audio waveform that is flat - a little at the beginning, but most at the end), which to me indicates that the frame rate in Kdenlive is incorrect. I exported the audio of that clip and it came to be 5:28;26, which is what I expect the clip length to be. Moreover, that is exactly the length of the same clip (both video and audio) that I get when I use Cinelerra and there is no period of flat audio waveform at start/end. Cinelerra reports a frame rate of 29.97 for the project profile as well.
This is the weirdest, most annoying thing and its rendering Kdenlive useless to me. I cannot tell though if the problem is isolated to Kdenlive or if it is the case with any program that relies on melt (MLT?).
I even trancoded the clip and forced a frame rate of 30 FPS and then imported it into Kdenlive but got the same results. Even ffmpeg reports that the frame rate is 29.97, so I know that I have the frame rate setting correct!