There are two things relating to PF rating on inverters.
One is output kVA load minimum tolerable power factor for output loads. HF inverters are usually limited on their output power factor loading due to their two-stage design with HV DC filter capacitor. Too much inductive loading can creating a problem with peak over-voltage on HV DC voltage point that can damage its filter cap or high voltage IGBT's. Common limit is no worse than a load power factor of 0.8.
Second is power factor presented on input AC when battery charging from AC input grid or generator. Some HF inverter/chargers just use regular rectifiers from AC input to HV DC point which results in poor power factor during charging from AC input. This is of more concern when charging through inverter/charger from a generator.
Low frequency inverters are much better at handling poor power factor loads and provide good AC input power factor during AC input battery charging.
In practice there are two types of poor power factor. One is due to high short peaks of output current loading on inverter caused by simple rectifier-filter AC to DC power supply appliances, like you might find on an VFD drive three phase inverter air conditioner. This just causes high peak currents resulting in more inverter efficiency loss and therefore less real output power capability.
Other type of poor power factor is due to inductive AC motors, like pumps and conventional air conditioner compressors. Because of the inductive component of load, the AC sinewave voltage peak occurs before the AC sinewave load current peak. There can actually be a short period of load current reversal during a portion of AC cycle. A HF inverter can have an issue with this short reverse current push.
In both power factor cases, the inverter efficiency will degrade causing greater inverter losses and internal heating at high loads.
Inverter, generators, and transformers are really rated for VA loading (called apparent power) not actually watts (real power) of load. When load power factor is 1.0, VA equals watts.