The principle shown in the video seems to be different than filling the boring bar with lead. The latter increases the mass, the former induce a dumpening due to the internal mass but mediated through the elastic rings. (Intuitively) the transfer function seems to be different because just increasing the mass simply shifts the frequencies at which the oscillations take place, while adding those elastic elements insert somewhere a constant factor (dumping) into the formula.
The grease and lead balls seems to be similar to the solution shown in the video, but cheaper and simpler, because the grease can't introduce any delay* but only a dumping factor (due to [the small] compressibility).
I wonder what happens to rigidity.
Remarks:
*The delay comes from the Newton's second law: F = m a = m (dv/dt). The "dt" argument introduces the "delay", or better a time shifting factor in the transfer function of the motion from workpiece on the spindle (in the case of the lathe) to the boring bar holder. We can use this transfer function to assess the stability of the system composed by the workpiece in rotation (as action) and the boring bar (as reaction) and a noise generator determined by the point of contact of the tool with the workpiece. This noise will induce oscillations that could increase in aplitude if the system resonates (i.e., it's not stable).
N.B. This is to explain my intuition, I do not know if this is the common way to model a system like this.

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, because the grease can't introduce any delay* but only a dumping factor (due to [the small] compressibility).
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