There are two ways of looking at this. One is the technical definition of an SLR doesn't specify that the lens must be interchangeable. The other is that an SLR without an interchangeable lens defies the whole point of having an SLR.
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 flip-down mirror that bounces light from the main lens into an optical viewfinder.
SLR cameras trade the inconvenience of the bulky mirror and pentaprism assembly for the benefit of allowing for interchangeable lenses while keeping the optical viewfinder.
The whole point of an SLR is to allow for interchangeable lenses without needing to change the lens used in the viewfinder, because it simply looks through the same lens. If you have a camera without an interchangeable lens, there is no reason to have a reflex mirror or to have the viewfinder look through the main lens.
My argument would strongly fall on the side of such a camera not being a proper SLR, for this reason, 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. It boggles my mind why they would do this for a camera with a fixed lens, though. You get all the disadvantages of the bulky mirror assembly and pentaprism, without benefiting from the whole reason that cameras started using these in the first place: interchangeable lenses. It is the opposite of the trend toward mirrorless system cameras, which ditch the bulky mirror and pentaprism assembly while keeping the interchangeable lens - a win-win situation for those who can manage to forego the optical viewfinder.
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. I can't imagine that cost-saving would be a real reason, since they elected to add an expensive mirror and pentamirror assembly when they didn't really need to.