this is how I always experienced mob tagging on vanilla. I have never seen this so called tag stealing on bosses even when I killed Kazzak or Azuregos with my guild back then. The bosses only reseted their tag when there was no-one else to kill. It didn't matter if the group was different.
If I died to a npc while the tag. was mine, it would not change until everyone in the threat table was dead. Most of times I died to mobs while a horde player helped me kill it and the tag would remain mine for me to loot and even get the experience.
The only tag stealing I ever heard of, was only when people mob tagged to get kill credit, pissing others off :P
However, I think there was a mechanic in place where if you dealt a certain damage % on the mob then everyone else, the tag would switch to you, but I do not remember where I heard of this.
Edit 1:
Retail mechanic: There is another mechanic that is called shared mob tagging that only happen per faction raid groups and works as the following: Person A joins raid A, then tags the mob. Person A leaves raid and joins raid B. Raid B now also had tag on the boss (Person A needs to be leader or have started the raid).
About that damage % tag switching, it occurs on NPCS and I think its like 70% hp.