It's very unlikely that double exposure could happen with a digital camera in the way it could occasionally occur unintentionally (and, often, intentionally) with film cameras. That's because there's no "film advance" mechanism in a digital camera. Each frame is read as a separate file, and there's no plausible way for them to get mixed up. If the electronics were so scrambled as to make that happen, you'd get a broken file, not a coherent overlaid image. Likewise, if you get any image at all from a faulty flash card, the result will be distinctively blocky (like this), not cloudy or ghost-like.

While some Pentax cameras do have a multiple exposure mode designed to give this kind of effect (and also HDR modes which could in some circumstances give a similar appearance), the S30 does not. It does have a "two-in-one" mode, but that clearly slices the frame in half rather than overlaying the two exposures.

The more plausible explanations here are:

1. The "ghost tour" had some sort of special effect.
2. The woman has done something in post-processing.
3. It's some other sort of artifact like lens flare which only looks like human figures if you are looking for that.
4. The photo doesn't actually exist and someone just enjoys telling ghost stories.

Keep in mind that before photography, ghosts were not usually described as having the diaphanous double-exposure look we associate with them today. That appearance doesn't come from folklore, but from early attempts at fooling people using, yes, double exposures. The technology has changed, and there are more advanced (and easier!) ways to doctor an image, but for some reason, we've held on to that idea of semi-transparent ghosts.

Particularly given the detail of "she did not recognize the figures", it seems like some degree of wanting there to be a ghost is involved. Without seeing the image or knowing the woman, I'd put my money on #4, or on #3 exaggurated into #4 by a strong wish to believe. And if you're friends, I think I'd just not push it. People really like their ghost stories (particularly, people who go on "ghost tours"), and it's mostly in fun, so actually getting serious about debunking the photo kind of ruins that.