The statement's point is pedagogical - you don't risk more by buying an option than you pay up front. It's also true - if someone were to offer you free option

The statement's point is pedagogical - you don't risk more by buying an option than you pay up front. It's also true - if someone were to offer you free options, you couldn't lose money by accepting them. This is distinctly different from, say, a future or a forward, which is an agreement with no money exchanged upfront (other than commissions and margin requirements).