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This is an answer, because it could not be inserted as a comment. The following code starts the check in a special case of a directed graph given by the divisibility relation on the integers from $1$ to $120$:

sage: g = DiGraph([[1..120], lambda i,j: i != j and i.divides(j)])
sage: checklist = []
sage: for v in g.vertices():
....:     in_v  = g. in_degree(vertices=[v], labels=True)[v]
....:     out_v = g.out_degree(vertices=[v], labels=True)[v]
....:     deg_v = g.    degree(vertices=[v], labels=True)[v]
....:     checklist.append( in_v + out_v == deg_v )
sage: False in checklist
sage: checklist == 120*[True]

So the checklist contains only the True value. This is ok. Which is the result for the graph T from the OP? Which is the method used to construct it? Is there a minimal example reproducing the same error / incompatibility?!