Why? When under the same or similar circumstances I am seeing 800mA from my own home-built solar charger.

The way I understand the charging process is the charger is tested by the phone along the way. First second or two, to see if it can supply more than a couple of hundred mA. The charge is kept at approx 500mA for a few seconds, I haven't timed it but it seems like around 5 seconds, maybe 10. There seems to be another check after this to see if the charger can supply more.

There are kernel messages seen in dmesg | tail at this time too.

The only way I can see this charger is supplying 650mA is because that is all it is able- / limited- to supply

1C is quite a significant charging rate.