I don't see any unfairness.

Okay, try running this and see if it changes your mind.

#! perl -slw
use strict;

our $N ||= 1e6;

my %stats;

my  @data = 'A' .. 'Z';

for my $n ( 1 .. $N ) {
    my @scratch = @data;

    foreach my $first ( @data ) {
        for my $j ( reverse $#scratch -2 .. $#scratch ) {
            my $r = rand( $j + 1 );
            @scratch[ $j, $r ] = @scratch[ $r, $j ];
            if( $scratch[ $j ] eq $first ) {
                my $r = rand $j;
                @scratch[ $j, $r ] = @scratch[ $r, $j ];
            }
        }
        ++$stats{ $_ } for @scratch[ -3 .. -1 ];
    }
    system 'cls'; printf "%8d\n", $n;
    printf "%s : %6d ( %+3d ) %s\n",
        $_, $stats{ $_ },
        $stats{ $_ } - ( 3 * $n ),
        '#' x abs( $stats{ $_ } - ( 3 * $n ) )
        for @data;
}
[download]

Over time, the variance should tend to converge towards zero for all choices, but every time I run this, one or two of the choices show no signs of converging. Indeed, their variance just seems to grow. Not mathematical proof of unfairness--I can't work out how to apply a Chi Squared test to this kind of data--but sufficient to convince me that there is something hookey.

BTW, you'll need a wide terminal to see the effect at it's best. Mine is set to 1000 wide. Setting a small font also helps as the numbers grow.