Are the factory black bilstein struts rebuildable?

No, the Glan nut is spot welded as per your pic.
From my experience, all JDM sw20's are welded, ADMs are not, hence are rebuildable.

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Carmikey

From my experience, all JDM sw20's are welded, ADMs are not, hence are rebuildable.

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I don't think it's as simple as that.
My ADM '90 model had the removeable gland nut struts, and I have seen early SW20 turbos that had them also.
I have also seen the welded top factory Bilstein struts on a Bathurst model, so I would assume from the factory.

89 - late-91 had removable inserts
Late-91 - 99 had sealed-for-life canisters.  Bilstein dampers were an option early on and got fitted as standard in Gen3.  Some had black paint, some had yellow paint, depending on spec.  If no labels are present, you can identify them visually, as the canister is significantly thicker above the mounting bracket for the hub.

Thanks for the replies guys...bugger!
Looks like I'm looking for a set of replacement rebuildable strut tubes.
Anyone got any?

I still have a set of the OEM Bilsteins that I retired from service a couple of years ago.  For interest sake, I decided to take the top off one of the perfectly good worn out rear struts.  The following pics show the tear down and a comparison of the standard Toyota insert against the Bilstein.
 

A few more pics

Lindsay for your info, if you want to do the job yourself here are some more pics comparing a gland nut strut to the sealed bilstein
You throw away all the guts from the gland nut strut and replace with sealed inserts.
I don't know about other brands but if you fit Koni's you can not reuse the old gland nut but must use the supplied Koni top nut.
You must also fit the split plastic washer on top of the strut to prevent damage to the insert from bottoming out on the bumpstops.
It is also advised to fill the void around the insert with coolant mix to assist heat transfer.
 
BTW, if you use lowering springs, be aware that the early model OEM bumpstop is thicker that the later models, so go for the later ones or you won't have enough bump travel.
 
 
 

Very interesting.