You can Rage and Wild Shape at the same time.
For reference, I'll quote and cite the two abilities.
A barbarian can fly into a rage a certain number of times per day. In a rage, a barbarian temporarily gains a +4 bonus to Strength, a +4 bonus to Constitution, and a +2 morale bonus on Will saves, but he takes a -2 penalty to Armor Class. The increase in Constitution increases the barbarian’s hit points by 2 points per level, but these hit points go away at the end of the rage when his Constitution score drops back to normal. (These extra hit points are not lost first the way temporary hit points are.) While raging, a barbarian cannot use any Charisma-, Dexterity-, or Intelligence-based skills (except for Balance, Escape Artist, Intimidate, and Ride), the Concentration skill, or any abilities that require patience or concentration, nor can he cast spells or activate magic items that require a command word, a spell trigger (such as a wand), or spell completion (such as a scroll) to function. He can use any feat he has except Combat Expertise, item creation feats, and metamagic feats. A fit of rage lasts for a number of rounds equal to 3 + the character’s (newly improved) Constitution modifier. A barbarian may prematurely end his rage. At the end of the rage, the barbarian loses the rage modifiers and restrictions and becomes fatigued (-2 penalty to Strength, -2 penalty to Dexterity, can’t charge or run) for the duration of the current encounter (unless he is a 17th-level barbarian, at which point this limitation no longer applies).
And then you've got the Druid.
Wild Shape (Su)
At 5th level, a druid gains the ability to turn herself into any Small or Medium animal and back again once per day. Her options for new forms include all creatures with the animal type. This ability functions like the alternate form special ability, except as noted here. The effect lasts for 1 hour per druid level, or until she changes back. Changing form (to animal or back) is a standard action and doesn’t provoke an attack of opportunity. Each time you use wild shape, you regain lost hit points as if you had rested for a night.
Any gear worn or carried by the druid melds into the new form and becomes nonfunctional. When the druid reverts to her true form, any objects previously melded into the new form reappear in the same location on her body that they previously occupied and are once again functional. Any new items worn in the assumed form fall off and land at the druid's feet.
The form chosen must be that of an animal the druid is familiar with.
A druid loses her ability to speak while in animal form because she is limited to the sounds that a normal, untrained animal can make, but she can communicate normally with other animals of the same general grouping as her new form. (The normal sound a wild parrot makes is a squawk, so changing to this form does not permit speech.)
What's probably driving your friend's claim is that Wild Shape is a Supernatural Ability.
Supernatural abilities are magical and go away in an antimagic field but are not subject to spell resistance, counterspells, or to being dispelled by dispel magic. Using a supernatural ability is a standard action unless noted otherwise. Supernatural abilities may have a use limit or be usable at will, just like spell-like abilities. However, supernatural abilities do not provoke attacks of opportunity and never require Concentration checks. Unless otherwise noted, a supernatural ability has an effective caster level equal to the creature’s Hit Dice.
During a rage, a character can use Supernatural abilities. Raging does not end any effect currently going.
A Druid/Barbarian isn't optimal, but you can absolutely turn into a bear and then rage. If you're wiling to waste a turn while raging, you can activate Wild Shape during a rage, but that's really sub optimal.