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I doubt Tigris was the only undefeated gladiator in history, but I'll address your 'in movie' questions:
1 - Proximo quite conceivably could have been defeated. You don't have to be killed to be beaten as a Gladiator. Indeed, many were not.
2 - 'the Spaniard' was undefeated, but not to conclusion. I.e. he could have been defeated before his 'retirement'. That was yet to be seen.
3 - 'propaganda' of the announcement. Truth doesn't matter, must exciting the mob.
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Ok, I stand corrected, but it does actually illustrate my point the Gaul could easily have been defeated, but not killed, yet in the days without the internet, easily could have had an 'only undefeated' myth made up about him. Hell, an entire WAR was fought because of the mistaken belief that Marcus Aurileus was dead (real history, not this movie)

Ali never retired undefeated. His decision losses in the first Frazier and Norton fights were years before his first retirement.

Ok, we know Proximo was given his freedom, but he could have been defeated but not killed (thumbs up etc).
We know that until that point Maximus (at the very least, but the Numidian as well so far as we know) were undefeated, but I would think being still 'active' makes them not undefeated/not defeated/yet to be seen type.
The Gaul, was (it seems) never defeated, and retired from the games, so a little 'special'.
It's similar (I think) to the fact that Mohammed Ali was a retired undefeated heavy-weight (until he stupidly came out of retirement) and would have had (at that time) a lot more respect as such than a current reigning, heavy-weight.
Just my opinion.

The speaker could have been lying as well.

That is a very good point. Thanks.

When I heard that line, I took it as the undefeated home-town gladiator. Gladiators that were brought in, such as Maximus, were the away team.

I'm not sure what to say, technically shy gladiator that of fighting and not dead is undefeated. Maybe it was just for Maximus to look more badass. Would've been silly for him to fight a 60 year old guy.

Rome had no more Gladiators till these games to honor the previous Caesar.
It's not impossible that he retired when Rome stopped having games.

Tigris had come out of retirement for the match, so he wouldn't be current.

I would assume that Tigris was the only current undefeated gladiator.