"It can take input of 19.5 kW of DC, but only output 15kWs of it?"
Correct.
"So is there no way to use all of the 19.5 kW, as in some DC charging batteries and some inverted to AC for load?"
No. But remember that the 15 kW output of the inverter can be split up in any combination of (DC) battery and (AC) load.
I tried to address this point just a few sentences later (the final one in that paragraph), to wit:
"We also discussed how the PV input specs in the spec sheets (for both the 12K & 15K) being higher than the inverter output represents the DC to AC ratio."
If you're not familiar with DC to AC ratio, I'll try to summarize as succinctly as I can. If I get this wrong, I'm sure there is someone here that can and will correct me. PV panel wattage ratings are given under ideal conditions, which - for all practical purposes - are rarely (if ever) reached. So inverters allow you to "oversize" your PV panel input to the inverter so that you can have the inverter maximize the available solar energy available without frying the inverter. This is where having an experienced solar engineer comes in quite handy. So, in this case (as long as you stick to the max voltage and amp limits per string), you can have as much as 19.5 kW of panels hooked up to the MPPTs to get to the 15 kW that the inverter can actually use. No matter how much you oversize your PV panel input to the MPPTs (up to the specified limits), if they happen to produce more than 15 kW of DC power, the MPPTs (Or is it the inverter electronics? It's one of the two.) "clip" the incoming power down to what the inverter can actually invert. I guess the most simple phrase that summarizes it is "real world wiggle room". Remember that experienced solar engineer I mentioned? He/she would take in all the factors of your installation (latitude, average high & low temps in all seasons, humidity, altitude, sq. footage available, required energy output, budget, etc.) and size the system with the right size, number, and output (etc.) of panels (and maybe batteries) so that you get as close to the required kWh on the
worst day(s) of the year without clipping (wasting) too much panel wattage on the
best day(s) of the year.
In all of my research so far, none of this is unusual. I could be wrong, but I think that about every inverter I've seen has a DC to AC ratio.
Bitte.