Your post made me curious so I looked for any references to studies or anything on the Happiness Project website. I found a post where Ms. Rubin sad the following:

As I say in my post, check out Haidt's Happiness Hypothesis.

Also look here, for something online: <link>

The study referenced doesn't exactly support her point, but more takes it as a given and references studies that do support it. In definitely seems to indicate that your belief that squelching anger is unhealthy is a myth. This is the concluding passage:

Our findings suggest that media messages advocating catharsis
may be worse than useless. They encourage people to vent their
anger through aggressive action, and perhaps they even foster the
displacement of aggression toward new, innocent third parties. In
our research, people who received procatharsis messages first
chose to vent their anger by hitting a punching bag, but then they
went on to show elevated aggression toward the person at whom
they were angry. They even showed increased aggression toward
an innocent third person. Pop writers may think they are offering
helpful, sage advice on affect regulation, but the effect of advocating
catharsis may be to cause a general increase in aggressive
behavior. Perhaps media endorsement of cathartic release should
come to be regarded as a potential danger to public health, peace,
and social harmony.

Like I said, this particular study doesn't prove anything, but it references other studies you can look at if you want evidence of what Ms. Rubin claims.