Exists only looks for keys, in your first example ALEX is a value, not a key.

I suspect you think your has looks like this:

(
  'AALIYAH'    => '',
  'AARON'      => '',
  'ABBE'       => '',
  'ABBEY'      => '',
  'ABBI'       => '',
  'ABBIE'      => '',
  'ABBIGAIL'   => '',
  'ALEX'       => '',
)
[download]

When in reality it looks like this:

(
  'AALIYAH'    => 'AARON',
  'ABBE'       => 'ABBEY',
  'ABBI'       => 'ABBIE',
  'ABBIGAIL'   => 'ALEX',
)
[download]