Yes, something needs to trigger it.

Thinking a bit more though, I was only thinking of a snowflake in the avalanche, rather than a snowflake falling on the top causing everything to fall down - like messing up the last card in a house of cards. If that's what they meant then it makes a little more sense, but still doesn't really hold true. 90% of all avalanche disasters are triggered by humans.

An avalanche requires that certain types of snowflake form a "weak layer" in the snow. Some snowflakes are kind of smooth on the sides, these don't have the jagged edges that hook onto other snowflakes. When a force is applied, this weak layer breaks and the snow on top of the layer slides down the slope. A single snowflake will not apply enough force to break the weak layer - the amount of force it applies would be negligible even compared to things like the wind. Something else will trigger the avalanche before a snowflake ever could.

The snowflake provides the conditions for an avalanche, but doesn't apply the force that triggers it.