wire gauge for dual driven appliance (solar inverter)
The NEC has no bearing on factory wiring within listed equipment

The gauge of factory wiring in listed equipment is governed by the applicable UL standards and by the testing UL conducts in accordance to those standards (usually various temperature rise tests) as part of the listing process, not by the NEC.  This is reflected in NEC 310.1:


  310.1 Scope. This article covers general requirements for
  conductors and their type designations, insulations, markings, mechanical strengths, ampacity ratings, and uses. These
  requirements do not apply to conductors that form an integral
  part of equipment, such as motors, motor controllers, and similar equipment, or to conductors specifically provided for elsewhere in this Code.


As a result of this, we must look outside the NEC for an explanation of this.  While I have not seen explicit provisions for these sorts of potential or control taps in what I have been able to read of UL 1741, the UL 508A standard for industrial control panels contains a provision in 41.1 Exception 1 that can be used for an argument by analogy in this case:


  41.1 The conductors of a control circuit tapped off the load side of the branch circuit protective device
  shall have overcurrent protection sized in accordance with the ampacity of the control circuit conductor as
  specified in Table 28.1 and Table 38.1.
  
  Exception No. 1: When the control circuit is tapped off a motor branch circuit protective device and the
  control wires do not leave the industrial control panel enclosure (such as when a start-stop button is
  provided on the enclosure cover) the motor branch circuit protective device provides the required
  overcurrent protection when its rating does not exceed that specified in Table 41.1.


Given that Table 41.1 in UL 508A-2014 permits a 14AWG control tap on a motor branch circuit of up to 100A in size and a 16AWG tap on a circuit up to 40A when the conditions of Exception 1 are met, I would say that the safety case for the potential tap wiring you see in your inverter works analogously to the logic behind the above quoted exception.