According to a site that specializes in Tungsten rings, they corroborate the jeweler's story and provide an explanation:
The size you are given is the size you would wear in a traditional fit ring. A traditional fit ring is flat across the inside of the band. Both Tungsten and Ceramic bands have a comfort fit inner band. All Tungsten Affinity rings have the comfort fit feature. Comfort fit bands are domed on the inside with the tightest point being the center of the ring gradually expanding in size towards the edges. *IMPORTANT Comfort fit tungsten rings generally fit 1/2 size larger than traditional bands. We recommend you order a 1/2 size smaller than the size you were given at the jewelry store.
So, yes, you will probably want to go with a half size smaller than your measured size. Though, I think you need to look a bit more. That same site that I found the explanation on seems to sell rings as small as a size 4. I'm not endorsing them as a company - they merely had the information I needed and, while there, I decided to see what their sizing looked like. They seem to be emphasizing that these rings are appropriate for both genders, not only men (who have been the traditional owners of these rings), so it makes sense that they would offer "extended" sizes as women's fingers on average are smaller in diameter.
Please note, as Tungsten can not be resized, you should be sure to find a seller with a liberal return policy in case the size you purchase is not good for you. Particularly if you're considering a wider band, you may need to go back up a half size to accommodate that. You haven't noted your gender so I'm not sure what sort of sizing ring they used. From that same page:
The second part to sizing is the band width. Band widths are measured in millimeters (MM) and for tungsten bands generally range from 4mm to 10mm. The width of the band will effect the how a particular size fits. The wider the band the tighter the ring will fit, whereas the more narrow the band the looser the fit. When sized at the jewelery store women are sized for more narrow bands, so our standard women's width is 6mm. Men are sized at a slightly wider 8mm band width.
Congratulations and I hope you are able to find a ring that works for you.