It sounds as if the person recommending $300,000 was talking about Personal Liability insurance.
A coop/condo/renters policy covers personal property (household furnishings, additions & improvements etc)as well as personal liability.
The personal property limit has to be set by the individual who knows what it would cost to replace his property as well as any additions & improvements to the apartment..
Students usually don't need more than $25,000 but that depends on what he/she has in the apt
$300,000 is fine for the liability aspect although I always recommend a higher limit which doesn't cost very much more.
Ask your broker/agent for suggestions and prices.