The cell of origin of human Barrett esophagus is still not identified. There are many interesting research on the subject like this one:

http://www.tandfonline.com/doi/abs/10.4161/15384101.2014.972875?url_ver=Z39.88-2003&rfr_id=ori%3Arid%3Acrossref.org&rfr_dat=cr_pub%3Dpubmed&#.VLVxHz8cTmQ

Various factors that arouse dysplasia before metaplasia could make the process of cell transformation unstable and perhaps not specific, especialy in the case of `Barret Esophagus` that involves consequence of contrversial acidic or alkaline relux metamorphosis. 

Thank you for the posts and the link of yours', Dr. Julianov and Dr.Shidi.

And yet, I wonder, if one washed his/her hands with an acidic soap day after day, would his/her epidermis turn into the columnar lining? Or, if one chewed a slice of limon every breakfast, would transform the stratified epithelium of his/her mouth into the intestinal one? (but not gastric one, of importance)

Interestingly, there is at least one more place where the stratified and columnar epithelia meet in the human organism: it is the cervix with its commonly known the cervical ectropion and the cervical carcinoma. And there are mucous glands too, of course.

The current "evidence" is pointing towards a pre-cursor cell in the gastric cardia. But there is also data suggesting the submucosal glands is where the "Barrett's stem cell" comes from.

Michael Quante and Janusz Jankowski's work provide some good data on the cells coming from the gastric cardia. This is one of the landmark papers of recent years:

Bile acid and inflammation activate gastric cardia stem cells in a mouse model of Barrett-like metaplasia.

Cancer Cell. 2012 Jan 17;21(1):36-51. doi: 10.1016/j.ccr.2011.12.004.

Quante M. et al.

It's a hot topic of debate of course.

Thank you, Oliver!

Indeed, some glandular origin seems to be much more probable than that from the basal layer of the squamous epithelium. By the way, from the very beginning I have scribbled this putative process on the pictures above.

I shall be reading the papers you referred here.

Andrey, I thought I may need to update my answer on this question...now that I've spent a lot of time researching the area and am currently writing up a chapter on Barrett's origin. 

The simple answer is: it's not entirely clear. What's very probable is that there is a common progenitor cell to both squamous epithelium as well as Barrett's. And the groups around Nick Wright (including Jankowski as a co-author) and co have some compelling data supporting this (Nicholson et al. Gut 2012, Leedham et al. Gut 2008). But the issue is that there is some human and moreover high-profile murine data (Wang et al Cell 2011, Quante et al Cancer Cell 2012) suggesting either the squamocolumnar junction / gastric cardia may be a potential source for the Barrett's progenitor cell. A problem is the comparability of the murine anatomy to that of humans. Equally, another issue is that in patients who have had an esophagectomy thus having their cardia and squamo-columnar junction removed Barrett's can still develop...and this would argue against the "true" source being in the cardia/SC-junction...another issue is that Barrett's glands are truly protean and a recent paper by Lavery et al (Gut 2014) suggests that the stem cell organisation and proliferative as well gene expression profile of Barrett's glands is very similar to that of pylori-type gastric glands...How this phenotypic resemblance can then be married with the concept of a specific "Barrett's progenitor" cell is not clear to me...but tends to point more towards the direction of a common Upper GI progenitor cell that will develop in a particular direction based on external pressure...

Hope this helps...it's just a realized that my original answer wasn't completely correct and didn't acknowledge the controversies surrounding this topic properly...