Skeptical about Mollers...  

I've not seen that design before, looks to be 70's or 80's, I'm sure someone here will be able to confirm the model.
That is the correct Moller makers mark.

Maybe
someone wanted to strengthen the chairs, after they've come loose?
strange...
The model is authentic, but the cross and plugs are in my opinion a later addition.

I think the cross bracing was added later.
Those are the dining variation of the Møller "Church Chair"---
"Moller Church Chair. (JL404)
N.O. Møller
1967
Description:
The JL 404 Stacking Chair
1. The JL 404 is Denmark's most widely used ecclesiastical chair. The chair has a frame in solid beech and a seat of woven cord.
2. Accessories such as a book crib or peg are available as standard.
3. The chair stacks up to 6 high and is designed to be placed into rows keeping a uniform look to the interior space.
Linking
Each chair is fitted with simple interlocking brackets that are paired together when the chairs are placed into a rows."
http://www.danish-design.com/manufacturers/mol/JL404/
Below is a link to a set of the dining chairs---with no cross bracing. I think they're quite handsome!
http://www.homeanthology.com/seating/single-gallery/17258999

It looks
that the chair has been repaired which is why the cross is inserted and you have dowles hiding the screws.
proceed with caution

.
Well, the cross bracing are unprofessionally added, the original model 404 you can find at the J.L. Møller website.
And by the way, it's not designed by Niels O. Møller, but by Jørgen H. Møller.
http://www.jlm.dk/

Thanks folks
I really appreciate the feedback on this, I can move on in finding a less butchered set of chairs. If it's too good to be true...
cheers,
Unfurnished