FindCycle with EdgeWeight in directed graphs

Following up on the discussion in Problem with EdgeWeight and FindCycle?, consider the simple directed graph:

graph = Graph[{1 \[DirectedEdge] 2,                2 \[DirectedEdge] 3,                3 \[DirectedEdge] 1,                     3 \[DirectedEdge] 2 },                 EdgeWeight -> {1 \[DirectedEdge] 2 -> 0,                               2 \[DirectedEdge] 3 -> -1,                               3 \[DirectedEdge] 1 -> 1,                                   3 \[DirectedEdge] 2 -> 1 },                 EdgeLabels -> "EdgeWeight", VertexLabels -> "Name"] 

A simple directed graph

Note this graph has two circuits of length 0: 1 -> 2 -> 3 -> 1 and 2 -> 3 -> 2

FindCycle[graph,0] 

returns:

{{1 \[DirectedEdge] 2, 2 \[DirectedEdge] 3, 3 \[DirectedEdge] 1}} 

It only finds one of the two cycles. Is the "all" in

For weighted graphs, FindCycle[g,k] gives all cycles with total weights less than k.

incorrect as well?