For software firm Tools4ever, signing with one of New York's start-up insurers in 2014 seemed like a good fit. Rates from nonprofit Health Republic of New York were $6,000 lower than those of competitors.

"It was a substantial amount of money that it was going to save our company," said Dean Wiech, president of the Long Island, New York-based firm whose experience was featured in a Health Republic television ad two years ago.