Caitiff, the Puzzling

Okay, so the matter of Caitiff being clanless came up at the NYC qualifier a couple of days ago. Someone was playing a weenie vote deck and tried to name caitiff for Con Boon. They found out that they couldn't do so. This re-raised some questions which I've never seen satisfactorily answered. Here they are:
1. Just to be clear, Caitiff is not a clan, correct?
2. Not all clanless vampires are Caitiff, correct? e.g. Shock troops is not caitiff.
3. I've seen discussions that involved reputable sources talking about a deck running Mukhtar Bey and third tradition to make caitiff babies ( I think they were for consumption by Al' Muntaquim). So, if caitiff isn't a clan, why does Third Tradition produce Caitiff babies, as opposed to generic, claness babies? The card says nothing about transferring nebulous keywords from the parent, just the clan.

So yah. I searched the rules, and all I found was a single mention which said that technically Caitiff are clanless. That's it.

1) Caitiff is a trait, not a clan. LSJ 11-21-2005

2) Not all clanless vampires have the Caitiff trait. LSJ 11-21-2005

3) New vampires sired by Caitiff are Caitff, by ruling. (Embrace, Third Tradition, etc.) LSJ 12-28-2001 and LSJ 01-02-2002

The really short version is... Cause LSJ said so.
[this post existed because the cancel button still doesn't work properly]

LSJ had nothing to do with it AFAIK. The source material states that Caitiff are clanless iirc.

Yes Kevin, and that's ALL it said. As printed, embrace, 3rd trad, etc have NO reason to transfer the Caitiff "trait" to the baby. I was just trying to figure out if there was some rule I missed, or if it was simply "because".

Embrace
Put this card in play; it becomes a non-unique vampire with 1 capacity of the same clan as the acting vampire.

3rd Trad
Put this card in play; it becomes a non-unique 1-capacity vampire of the same clan as the acting vampire.

So, since Caitiff are clanless, what would you have the card do?