Undergrad Applicability of Furry's theorem

[CAF123]

The diagram below, together with its reversed fermion flow diagram counterpart, collectively sum to zero due to Furry's theorem. I just wanted to understand why this is the case.

1)There are two gluons and one photon attached to the internal line so this is 3 coupled vector current insertions (1 QED and 2 QCD).

2) The blob represents a hadronic state. Why does the diagram contain a fermion loop coupled to the 3 vectors? I thought the blob always stood for arbitrary complicated soft dynamics that we are naive about and just 'put under the rug' so I don't see why it necessarily must be a simple closure of the fermion line shown.

 

[CAF123]

I understand now the answer to the original question asked. But I was also wondering, and perhaps this is a simpler question, is Furry’s theorem applicable for both off shell and on shell photons/gluons attached to a fermion loop? Since it is usually applied at the loop level I would say yes and I don’t see any reason why not with regards to the time ordered correlator of currents definition.