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First, note this only applies when the line to the input power source is long enough to have significant inductance.  If the power source is on the same circuit board, then this isn't an issue.

They are modeling the input power feed like this:

<img src="https://electrical.codidact.com/uploads/kmqefdtd4nej6md0nql3f2b4a5tr">

This is basically an L-C tank circuit with no way to dissipate any energy.  Once a transient starts it ringing, there is nothing to make the oscillations die down.

One way to dampen ringing is to add series resistance to C1.  What they are saying is that ceramic capacitors are too ideal in this regard, and have very little effective series resistance.  However, you don't really want any series resistance for the purpose of providing a low impedance input voltage to the buck converter.

Their solution is to add more lossy capacitors across C1.  That way C1 continues to keep the input power feed to the buck converter low impedance, since it is directly in parallel with it.  The additional capacitor will have more effective series resistance, which will only matter when the voltage across C1 is changing.  That's exactly what you want to dampen any ringing.

They are counting on the non-ideal characteristics of electrolytic capacitors, in this case the relatively large effective series resistance.  The effective series capacitor-resistor combination becomes a snubber.

You could add your own snubber with a more ideal capacitor and deliberate series resistance added to create the same effect.  If you really care about this issue, then that's actually a better approach.  Relying on non-ideal and unspecified parameters of component is bad practice.  Unless your electrolytic capacitor datasheet specifies a <i>minimum</i> guaranteed ESR, using one as advised by TI is technically out of spec.