There are two ways of looking at this. One is that the technical definition of an SLR doesn't specify that the lens must be interchangeable, so technically you could have a fixed-lens SLR. But the other way of looking at it is that an SLR without an interchangeable misses out on a big reason for why you would have an SLR in the first place.
To borrow from another of my answers, the technical definition of SLR is in its name. SLR means single lens reflex:
Single lens means that instead of having a separate lens and light path for the viewfinder, the viewfinder looks through the main lens.
Reflex means that there is a (usually flip-down) mirror that bounces light from the main lens into an optical viewfinder.
There's nothing present in that which indicates that an SLR must have interchangeable lenses.
However, SLR cameras trade the inconvenience of the bulky mirror and pentaprism assembly for the benefit of being able to attach any arbitrary lens while still allowing the optical viewfinder to function. If you have a camera without an interchangeable lens, there is no incentive to have the bulk of a reflex mirror in order to have the viewfinder look through the attached lens.
My argument would strongly fall on the side of such a camera not being a proper SLR, because it would defy the spirit of what an SLR is designed to be able to do. But you are free to disagree.
The Olympus E-10 is described by Wikipedia as being an SLR, because apparently it does have the viewfinder that looks through the main lens, complete with reflex mirror, that defines an SLR. As for why it does, I have no idea. To me, it seems that you get all the disadvantages of the bulky mirror assembly and pentaprism, without benefiting from the interchangeable lenses that this design allows.
If I had to guess, I'd say the reason that the Olympus E-10 goes to the trouble of having a flip-down mirror when it doesn't offer an interchangeable lens is marketing purposes: so they can market it as a DSLR. It doesn't seem to me that cost-saving would be a significant reason, since they elected to add an expensive mirror and pentamirror assembly when they didn't really need to.