The problem is not absent at sync tip or the level of the back porch, it is just lower there than at the white levels.
What I see in the problem "signal" is that it is demonstrating what is called differential gain. Differential gain in a circuit occurs when the gain is a function of the DC level. It is a frequent problem with the chroma component of composit video, but can occur in the luminance signal too. There are test waveforms to detect just this problem.
Your clamping may, actually probably does occur inside that chip. It is almost a requirement of any composit video processing. Often the clamping signal is derived from the luminance signal after the composit video is separated into the two components (luminance and chroma). But I will say it again, this does not look like any clamping problem I have ever seen.
Did I ever say it was a "clamping problem"?
My point was that, far from a "fault" the clamps (if present) were working as they should.
I have seen very noisy signals where clamping had been applied, with just as in this case, some residual noise remaining.
In video stabilising amplifiers, this can be removed by stretching the syncs & clipping them, but usually if the signal is that noisy, it is unuseable, even though functional syncs & blanking can be restored.
In this case, however, it seems the noise was present on the DC supply, so was still present to some extent no matter what is done within the chip.
"Differential Gain'?-----Yes, I am familiar with this concept, having tested video equipment & TV transmitters for this many times over decades.
Interestingly, in Australia, a distinction is made between (1)"Differential Gain" which is related to, & tested with a stairstep luma signal with a constant level of chroma carrier superimposed on it, & (2)"Line Time Luma Non Linearity" which can use a 1MHz signal superimposed upon a stairstep, or more commonly, a plain stairstep where the video output of the DUT is differentiated & the height of the resultant "spikes" compared to each other on a special graticule.
The signal for (1) is also used to measure "Differential Phase", where colours in the displayed image may be displayed incorrectly at various luma levels.