Why does VertexComponent not return all vertices at distance <= 3?

Something seems broken. As a workaround you might do something like:

gg[1] := NeighborhoodGraph[g, 50, 1]

gg[k_] := NeighborhoodGraph[g, gg[k - 1], 1]

HighlightGraph[g, gg[3], GraphHighlightStyle -> "Thick"]

Here's an alternate implementation of VertexComponent using AdjacencyMatrix:

vertexComponent[g_, v_, n___] := Module[{vec = initialVector[g, v, n]},
    ivertexComponent[g, v, vec, n] /; vec =!= $Failed
] /; ArgumentCountQ[vertexComponent, Length @ Hold[g, v, n], 2, 3]

initialVector[g_, v_, n___] := Module[{vl = VertexList[g]},
    Which[
        MemberQ[vl, v],
        Boole[Thread[vl == v]],

        ListQ[v] && ContainsAll[vl, v],
        Boole[MemberQ[v, #]& /@ vl],

        True, 
        Message[vertexComponent::inv, HoldForm[OutputForm @ vertexComponent[g,v,n]], v, "vertex"];
        $Failed
    ]
]

ivertexComponent[g_, v_, vec_, n___] := Module[{p, vl = VertexList[g], a},
    p = Replace[{n},
        {
        {i_Integer?NonNegative} :> i,
        {} -> Length[vl],
        {x_} :> (Message[vertexComponent::inv, HoldForm[OutputForm @ vertexComponent[g,v,n]], x, "parameter"]; $Failed)
        }
    ];

    (
        a = AdjacencyMatrix[g] + IdentityMatrix[Length[vl], SparseArray];
        Pick[vl, Unitize @ MatrixPower[a, p, vec], 1]
    ) /; p =!= $Failed
]

For your example:

vertexComponent[g, 50, 3]

{17, 26, 27, 28, 29, 30, 36, 37, 38, 39, 40, 41, 42, 47, 48, 49, 50, 51, 52, 53, 58, 59, 60, 61, 62, 63, 64, 69, 70, 71, 72, 73, 74, 75, 82, 83, 84}

Comparison:

Complement[vertexComponent[g, 50, 3], VertexComponent[g, 50, 3]]

{42, 69, 75}