The need for the pre-charge circuit in the batteries that he discusses is because of the inrush current of the inverter. I believe he even demonstrated this in the video when talking about proper power on procedure.
Further, even when the proper procedure is followed and the compressor load is turned on, there is effectively another inrush current event which trips the fault detection - thus the alarm condition. With more batteries in parallel the inrush load is shared between the batteries and thus doesn't trigger the fault detection or alarm.
You should be able to find plenty of info about inrush current via a search here and on the internet in general, but the best advice will be from the suppliers of the batteries and inverters you are working with.
Another related term for batteries that you might want to research is "internal resistance". There are many other installation and usage related factors that come into play as well, but these are probably the main ones.