Being somewhat more awake, I note that the Hlog graph does show some form of line defect.
Notice the pronounced "roll" and "hump" when transitioning to the higher frequencies?
(No doubt that Asbokid will upload an edited version of the image, with a dashed blue line showing the expected path of the curve! 
)
I might pass on that one! Though the kinky curve is interesting. A measuring quirk but no evidence of a fault as such.
Recall what attenuation is.. a gauge of signal strength. It is obtained by measuring the amplitude of a signal at two points - at the transmitter and at the receiver. Those two amplitudes, measured as voltages Vt and Vr, are then divided (Vr/Vt), to obtain a ratio. The voltage ratio is typically converted to a (logarithmic) decibel (dB) scale with 20log
10(Vr/Vt)
The near-end (the DSLAM a.k.a. the VTU-C) and the far-end (the CPE modem or the VTU-R), need to know the attenuation for the individual tones in each band (upstream bands and downstream bands). So that involves an exchange of information (the TX powers) to calculate those ratios.
There are two obvious explanations for the "kinks", or maybe a combination of two explanations..
i) the amplitude measurement circuits in the CPE and in the DSLAM are not calibrated with each other; or
ii) the line has propagation characteristics which are different for each end. More attenuation in one direction than the other. This seems counter-intuitive.. A line performs the same in both directions, yeh? Not necessarily. iirc, this is called the distal(?) heterogeneity of a transmission line.
A transmission line for FTTC - the so-called local loop - is usually comprised multiple segments of different cable types - drop cable, one or more D-side cable bundles, and perhaps a short patch cable to the DSLAM linecard. At each point where those segments meet, there will be an impedance mismatch. Since the mismatch points are not equidistant from each end of the loop, the propagation properties will not be homogeneous. Reflection losses, for example, could more pronounced in signals incident from one end of the loop, than from the other.
That is why line engineers are encouraged to test a line from both ends.. A fault might not be obvious from tests at one end.
Though probably the most likely explanation for the kinks is (i).. the signal strength measurement circuitry of the DSLAM and the CPE is not well calibrated, or not that precise.
cheers, a
