In theory you would be correct. The reality is that if you buy new Starline 38 LC brass, it is merely shorter 38 special.
Which is not correct for a 38 LC. Brew up a middling load in new 38 LC Starline brass and run a few through a factory 1895 Colt 38 LC.
It'll split brand new cases...the chambers are too big.
If someone could get OEM 38 LC ammo and try it in a 38 Spl...that would be interesting to see if it would fit at all.
Wiki is merely folks offering their learned ( sometimes) opinions.
Needs fact checking usually.
The bullet dia is off as well, have to run HB PL 38 spl pills to get a seal in a 38 LC.
Not meaning to offend of course, but the wiki info is a little 'loose' factually.
Easy

I have a bunch of old ammo that was given to me, someone's old collection. I don't collect myself but it helps me check things.
Anyhow, there is an old 38 colt cartridge, lead bullet has gone white, headstamp is wraco - so guessing 60s?
Pulled 5 differentl revolvers from the upcoming export, mostly mod 60, but also some others. All 38sp marked, not 357. 38colt fits in all of them, so the size difference is within tolerances for factory chamberings and factory ammo.
I'm sure you could chamber 38sp carefully in such a way as to fit 38sp but not 38colt or sw and leave a visible mark to show the chambers are long for sp and not others but it's up to the lab to accept that. Also remember the wording of the 'antique letters' - 'based on the information provided' so they reserve the right to say the gun is not antique at a later time, say it's not when you get dragged into court.
I'm now thinking a letter from a gunsmith stating the chambering was done using a 38sp reamer and tested to accept 38sp would go a long way too. But then what kind of repercussions might that gunsmith face if the lab disagrees in front of a judge? Would that letter have to be from a CFO licensed gunsmith?
Can of worms

Would I be interested in trying this just because I enjoy pushing the boundaries... Yes! If I find a frame or an otherwise broken revolver needing a new barrel an cylinder. I think step 1 would be to try some dummy chambers to see if I can make them take 38sp only... Anyone have a broken antique saa? (easier to try with one of those first) Or, now that I'm thinking of it, non antique? But still first gen and preferably 41, though 45 will probably be fine just to try the conversion?