Here is a counter-example from ?FindInstance
to that statement.
Let us consider
FindInstance[ x^2 + y^2 + z^2 <= 1 && 9 z^3 == 2 x - 5 y - 7, {x, y, z}, Reals]
{{x->45/128,y->-(1/2),z->-(3/4)}}
and draw it by
a = RegionPlot3D[ x^2 + y^2 + z^2 <= 1,{x, -1, 1},{y, -1, 1}, {z, -1, 1},PlotStyle -> Opacity[0.5]];
b = Graphics3D[{PointSize[Large], Red, Point[{45/128, -(1/2), -(3/4)}]}];
c = ContourPlot3D[{9 z^3 == 2 x - 5 y - 7}, {x, -1, 1}, {y, -1, 1}, {z, -1, 1}];Show[{a, b,c}]

We see nothing special/interesting for Point[{45/128, -(1/2), -(3/4)}]
.
PS. The same conclusion for the results of FindInstance[ x^2 + y^2 + z^2 <= 1 && 9 z^3 == 2 x - 5 y - 7, {x, y, z}, Reals,5]
.
PPS. FindInstance[x^2 + y^2 == z^2 && x > 0 && y > 0 && z > 0, {x, y, z}, Integers]
{{x -> 8, y -> 6, z -> 10}}
FindInstance[x^2 + y^2 == z^2, {x, y, z}, Integers, 3]
{{x -> 0, y -> 980, z -> 980}, {x -> 975156, y -> -3254045,
z -> 3397019}, {x -> -2952, y -> -26486, z -> -26650}}