It might easily be a simple case of a misunderstanding but then again maybe not we will possibly never know. Even though discussion of rates is for the most part a no no it never hurts to verify the length of the session and it might not hurt to ask if the information on their site is current and accurate. It is a simple way to make sure that there are no misunderstandings.
We all do things different and with some if you schedule an hour then expect to pay for the hour regardless of how long you are there, but some those that offer a 1/2 hour session then some might only ask for that. It just depends on the expenses involved for the provider. I use to not offer a 1/2 session but now I do based upon the average time a hobbyist was there but that is just me.