Interesting - I just emailed a tif to myself (as a .tif, then I noticed that the iPhone specs page lists .tiff, not .tif, so even though both extensions refer to the same file format, I tried .tiff as well). In both cases, when I tapped the attachment in the email, I got the spinning wheel, not the image (waited nearly a minute for a <50 KB image).
Then, I tapped the Reply arrow at the bottom, and since Save Image was an option, I tapped that. In the Camera Roll, I could see a fragment of the tif image. When I returned to the emails, I could view the tif (and tiff) images inline in the emails. So, I then sent a different tif to myself, and this time, when I tapped on the attachment it downloaded and opened normally.
Seems to be a bug, hopefully this workaround will help you...