Yes and no. You still have all their details to do as you wish. You could say the same about eBay to a certain extent.
I personally prefer the Amazon model. They only accept bonafide businesses, you are rewarded for unique products and most importantly your reputation. As a result it can take months to get established on Amazon and this also clears the eBay rejects out!
It's also a lot less hassle, you get paid, a much better quality customer, higher retail prices, higher margins, easier and quicker to process orders and the list goes on.
Our best selling product costs less than 50p and sells for over £12 inc postage. We sell so many we are talking to Amazon Fulfilment to do the fulfilment for just this product. Try doing that on any other selling platform especially competing with the ***** on ebay! (apart from a your own website).