Apple care free first two weeks?

I've never read anything about AppleCare being free for the first two weeks. Two free weeks would not add much of anything to the warranty and technical support coverage you already get when buying a new phone from Apple.

Here's what Apple says on the iPhone 13 page on their site:

"Every iPhone comes with one year of hardware repair coverage through its limited warranty and up to 90 days of complimentary technical support. Both AppleCare+ and AppleCare+ with Theft and Loss extend that coverage and give you additional features such as 24/7 priority tech support and accidental damage protection."

Cancel or change the payment method for your AppleCare plan - Apple Support

"If you paid in full upfront for your AppleCare plan … If you cancel your AppleCare plan within 30 days of your purchase date, you’ll get a full refund, minus the value of any service already provided."

I don't see any mention of a refund if you sign up for an AppleCare plan that is billed on a monthly basis – and then decide to cancel it.

Sounds to me like the sales person may not have known what he or she was talking about.

The sales person was misinformed, and you may have been charged for a service you don't need. Every iPhone has at least a one year warranty with no additional charges. You can purchase additional coverage for additional fees: Buy an AppleCare plan - Apple Support

Did you buy it from an authorized Apple retailer? It’s odd that AppleCare would be free for 2 weeks in any situation. There is no real way to try it out in 2 weeks unless you have a covered issue in that short of a time. The salesperson may have signed you up for their own plan since ApoleCare+ is $7.99 a month for the iPhone 13 or $11.49 for the Theft and Loss version. Might need to read through all of your agreement info or speak with the place you purchased from for more info