You are paying for a copy of the site. The code they used will be a collection of scripts and modules gathered together from various project and other sources. It's not 100% bespoke to you. Nobody builds a site from scratch. For example, if you have a payment portal then they will be using the script supplied by the payment processing application. You don't own this script. If you have a contact form it will used standard validation scripts and processing functions. The CSS isn't yours anymore than the php or asp is yours. Even the way information is passed to the database is just normal everyday code.
What you will own the theme, the images and content and possibly some of the backend tools. But that's about it.
That's a very simplistic way of looking at it tbh. Bespoke generally means "a custom build" as opposed to an implementation of a commercial product; thats built from the ground up based on requirements.
That can involve a framework or common class libraries (i.e. Code Igniter or Zend do not make it less bespoke) - both a solution thats coded from the ground up with no framework and a solution thats built from the ground up from a framework are bespoke. I know a fairly big social network that's built on CodeIgniter and you wouldn't call it anything less than bespoke.
Whether they own their site (as produced) is the question they need to know; if so then they are free to install it and use it however they wish. So it comes down to the agreement.
I can only use myself as an example as I don't believe we are unique in the ownership sense - I believe our approach is fairly standard.
When we build bespoke websites we have a framework which we use - unless the client states that a framework should not be used. It's a common framework that includes a core and various libraries that are designed to achieve certain things (for example a caching class for cache management, an imaging class for GD imaging routines and so on).
So each bespoke site we develop will share common code as they are based on the same framework. But then they have the implementation which makes them look very different. So two bepoke sites we develop will share a common heart but everything built around that will be unique to them.
When we contract they own the source; even though two sites will share some level of common code. The way we do it is that the license to the framework is owned by them and the code which we create to develop the product is owned by them.
Solves the problem and I would imagine that's how most bespoke site ownerships are handled; full and unlimited license to the framework and ownership of code built around it is effectively code ownership.
Of course then you have any open source stuff such as jQuery but that being open source is a done deal anyway.
So to assume that a client will never own a bepoke application is simply untrue. Whether they own it or not is dependent upon the providers terms not whether a framework was used.
Also if the OP wants to discover whether their application is truely bespoke and original - and to what extent; the solution is fairly straight forward; get an independent code audit. Not foolproof but it can reveal insights.
As to whether the site can go on a DVD; of course it can. It won't work from the DVD but the sources, database etc. can be packaged onto a DVD for them. They would admittedly have to upload all that to a server and set everything up. I suspect that's probably what they mean.
We and most providers I know provide sources via a repo though (i.e. SVN); the client logs in and downloads their sources. Any developer can then install it. I assume the CD/DVD thing is just different approach to the same thing (and kind of pointless really).