Hi,
The input current of an Opamp is near zero, thus driving an Opamp is the easiest thing to do.
But in your case it's driving 10k against about 1.8V.
Now that the INA can source 15mA ... this is no problem. The INA can sink about 400uA .. no problem, too.
I wonder why you are concerned about accuracy/precision. Usally 12V is a supply voltage...this means: not very accurate but noisy. but here it us used as reference voltage. Not even a noise filter is installed.
Also there is a diode at the output .. it's voltage drop varies with temperature and current.
Klaus