I was able to isolate the problem with BarLegend
in v.10.0.0. Yes, it is clearly a bug.
Let us see the how the thin grey lines are implemented:
Cases[
ToBoxes[BarLegend[{"DeepSeaColors", {0, 1}},
LegendLayout -> "ReversedColumn"]], _LineBox, Infinity]
{LineBox[
NCache[{{-(15/2), 225/2}, {15/2, 225/2}, {15/
2, -(225/2)}, {-(15/2), -(225/2)}}, {{-7.5, 112.5}, {7.5,
112.5}, {7.5, -112.5}, {-7.5, -112.5}}]],
LineBox[{{7.5, 112.5}, {7.5, -112.5}}],
LineBox[{{{7.5, 112.5}, Offset[{4., 0}, {7.5, 112.5}]}, {{7.5, 67.5},
Offset[{4., 0}, {7.5, 67.5}]}, {{7.5, 22.5},
Offset[{4., 0}, {7.5, 22.5}]}, {{7.5, -22.5},
Offset[{4., 0}, {7.5, -22.5}]}, {{7.5, -67.5},
Offset[{4., 0}, {7.5, -67.5}]}, {{7.5, -112.5},
Offset[{4., 0}, {7.5, -112.5}]}}],
LineBox[{{{7.5, 101.25},
Offset[{2.5, 0.}, {7.5, 101.25}]}, {{7.5, 90.},
Offset[{2.5, 0.}, {7.5, 90.}]}, {{7.5, 78.75},
Offset[{2.5, 0.}, {7.5, 78.75}]}, {{7.5, 56.25},
Offset[{2.5, 0.}, {7.5, 56.25}]}, {{7.5, 45.},
Offset[{2.5, 0.}, {7.5, 45.}]}, {{7.5, 33.75},
Offset[{2.5, 0.}, {7.5, 33.75}]}, {{7.5, 11.25},
Offset[{2.5, 0.}, {7.5, 11.25}]}, {{7.5, 0.},
Offset[{2.5, 0.}, {7.5, 0.}]}, {{7.5, -11.25},
Offset[{2.5, 0.}, {7.5, -11.25}]}, {{7.5, -33.75},
Offset[{2.5, 0.}, {7.5, -33.75}]}, {{7.5, -45.},
Offset[{2.5, 0.}, {7.5, -45.}]}, {{7.5, -56.25},
Offset[{2.5, 0.}, {7.5, -56.25}]}, {{7.5, -78.75},
Offset[{2.5, 0.}, {7.5, -78.75}]}, {{7.5, -90.},
Offset[{2.5, 0.}, {7.5, -90.}]}, {{7.5, -101.25},
Offset[{2.5, 0.}, {7.5, -101.25}]}}]}
Let us visualize them:
Graphics[%]

We see that the left line is simply absent. Why? Because the second line LineBox[{{7.5, 112.5}, {7.5, -112.5}}]
should have negative X coordinates in order to be placed on the left:
Graphics[{Line[NCache[{{-(15/2), 225/2}, {15/2, 225/2}, {15/2, -(225/2)}, {-(15/2), -(225/2)}}, {{-7.5, 112.5}, {7.5, 112.5}, {7.5, -112.5}, {-7.5, -112.5}}]],
Line[{{-7.5, 112.5}, {-7.5, -112.5}}]}]

So the source of the problem is now clear: the developer just forgot to change the sign of the coordinates of this line when implemented LegendLayout -> "ReversedColumn"
on the basis of already implemented LegendLayout -> "Column"
.
{19, 19}
in MMA 10. $\endgroup$