Model HABTM Model Referencing Original Model - php

Question

I have a Team model that is HABTM Match and when I pull the data for a specific Team, I ask for the related Teams for those Matches, but Cake only returns the data for the original Team.
How can I get all the Teams (the opponent) for that Match without looping through the results and pulling them that way?
I am having the same issue with the Team HABTM Player association as well. When I pull a Player, Cake will not return any of the associated Players (teammates) for the linked Team.
My schema:
CREATE TABLE IF NOT EXISTS `matches` (
`id` int(10) unsigned NOT NULL AUTO_INCREMENT,
`tournament_id` int(10) unsigned NOT NULL,
`name` varchar(255) NOT NULL DEFAULT '',
`created` datetime NOT NULL,
PRIMARY KEY (`id`),
KEY `tournament_id` (`tournament_id`)
) ENGINE=MyISAM DEFAULT CHARSET=utf8 ;
CREATE TABLE IF NOT EXISTS `matches_teams` (
`id` int(10) unsigned NOT NULL AUTO_INCREMENT,
`match_id` int(10) unsigned NOT NULL,
`team_id` int(10) unsigned NOT NULL,
PRIMARY KEY (`id`),
UNIQUE KEY `match_id` (`match_id`,`team_id`)
) ENGINE=MyISAM DEFAULT CHARSET=utf8 ;
CREATE TABLE IF NOT EXISTS `players` (
`id` int(10) unsigned NOT NULL AUTO_INCREMENT,
`name` varchar(255) NOT NULL,
PRIMARY KEY (`id`)
) ENGINE=MyISAM DEFAULT CHARSET=utf8 ;
CREATE TABLE IF NOT EXISTS `players_teams` (
`id` int(10) unsigned NOT NULL AUTO_INCREMENT,
`player_id` int(10) unsigned NOT NULL,
`team_id` int(10) unsigned NOT NULL,
PRIMARY KEY (`id`),
UNIQUE KEY `player_id` (`player_id`,`team_id`)
) ENGINE=MyISAM DEFAULT CHARSET=utf8 ;
CREATE TABLE IF NOT EXISTS `teams` (
`id` int(10) unsigned NOT NULL AUTO_INCREMENT,
`tournament_id` int(10) unsigned NOT NULL,
`name` varchar(255) NOT NULL,
`seed` smallint(2) DEFAULT NULL,
PRIMARY KEY (`id`),
KEY `tournament_id` (`tournament_id`),
KEY `seed` (`seed`)
) ENGINE=MyISAM DEFAULT CHARSET=utf8 ;
My query:
$this->Team->recursive = 3;
$team = $this->Team->read(null, $id);
$this->set('team', $team);
I have also tried:
$this->Team->contain(array(
'Match' => array(
'Team',
),
));
$team = $this->Team->read(null, $id);
$this->set('team', $team);
The results ($team):
array (size=4)
'Team' =>
array (size=5)
... team data ...
'Match' =>
array (size=2)
0 =>
array (size=9)
... match data ...
'MatchesTeam' =>
array (size=3)
'id' => string '1' (length=1)
'match_id' => string '1' (length=1)
'team_id' => string '1' (length=1)
// there should be an array for 'Team' here
// that contains the opponent team
1 =>
... more match data with same missing 'Team' array ...
... other related models ...