Is it true, that the solar inverter should be "under-dimensioned"?
It depends on the region you are living. The peak power of solar panels is rated under laboratory conditions, called STC (standard test conditions). In quite a few regions worldwide the rated peak power of the solar panels will not be achieved in reality. In other words, the output of the system is below the rated peak power.
This is typically true for central Europe in countries like UK or Germany where sunshine is moderate and if your roof orientation is not perfect (i.e. west or east orientated roof). In these countries the nominal power of the solar inverter can be ~5% lower than rated power of the solar panels. For example if your solar panels have a rated nominal peak power of 20 KWp, your inverters can be dimensioned to 19 KW. This makes your system cheaper without an reduction of the annual output.
Always make sure that the current and especially voltage match the operating range of your solar inverter. If the input voltage is too high, the inverter will be inevitably damaged.