If you need to build a web service that needs to use SSL I highly suggest that you use your own domain and your own SSL certificate (buy one) if you are going in production with it. If you just test/play around - than you can safely use the default provided one.
And you are correct about default provided one - you get a (free) SSL for your azure web site as long as it is only bound to the default XXX.azurewebsites.net
domain. However the certificate you get there is a wildcard certificate issued to *.azurewebsites.net
. I would not use it if I have to go for a production service!
If you are to use SSL features of Azure Web Sites with your own domain and certificate, check out the Pricing and requirement pages. There are important things to note!