I believe the more accurate claim would be: inserting ANY material between the cartridge and tonearm will change the mechanical impedance between the cartridge and its support (the tonearm). It is not possible for any cartridge designer to anticipate the mechanical impedance between their own cartridge and the customer's headshell since they have no control over the material and design of the headshell used. A change in mechanical impedance can be audible (for better or worse).
To your point,
@mtemur, adding any additional body to an assembly reduces overall rigidity, even if that inserted body is diamond. In other words, the fewer material joins in an assembly, the better - all other things being equal - when aiming for high rigidity. As a result, adding a shim is the wrong way to go.
HOWEVER, not all design elements weigh equally on our listening experience. I am convinced - as are my clients - that introducing our corrective shims to hit optimal playback angles results in far better performance than not having a corrective shim at all.
When a client has less than 1 degree SRA/VTA error, I offer them the prospect that they could get by without a corrective shim and instead hit their targeted corrective angles using the WallyReference single blades. Some take me up on the offer, but most cartridges need much more correction than this.