There are a lot of nasty germs in tanks.
The bacterium that your Mom is referring to is Vibrio. It's rare, but we experienced a nasty outbreak of it many years ago. It all but wiped us out (bad shipment of fish).
It's a similar bacterium to that which causes TB, but I'm not positive that it's the same - I've never heard of anyone contracting TB from their aquarium.
Another nasty is Mycobacteriosis. That can cause a nasty infection in people and it takes forever to heal, irrigation of the wounds daily with saline, and a big nasty regimen of antibiotics. I have a friend who had this once, and it was miserable. One thing that one should always do when working in a tank, is take a moment to wipe the rim/trim before putting an arm in. Salt buildup around the rim can rough up the skin on one's arm, and open the door to infection. This happens to a lot of people. My old boss used to get a rash occasionally on his arm, on the inside of his arm up near the armpit, because of that very activity - salt roughed the skin a bit raw and whatever bacteria were there, had a gateway. Some people are more sensitive to this than others, but it's a good safety practice to wipe away salt before starting - an ounce of prevention is worth a pound of cure. After seeing his rashes, and hearing about others who contracted some pretty serious infections, for me, it's automatic to wipe the rim first, whether I see caked up salt or not.
It's also a good practice to wash hands/arms after being in the water, and especially after handling corals. All corals produce toxins as a defense mechanism, and some are pretty nasty. Palythoa and zoanthids make some of the worst toxins. Palytoxin in particular is very nasty, and it's one of the most complex carbon chain molecules on the planet. I saw a lecture at SWU back in 05 where a scientist explained it all - bottom line, it's really really bad to ingest this stuff. Always wash. I know of people who have ingested it or even inhaled it and have become really sick. One fellow on RC a few years ago, tried to eradicate some zoas by taking them outside and pouring boiling water on the rocks. He accidentally inhaled the steam and ended up in hospital and nearly died. He now has to use a rescue inhaler regularly, and he never had any breathing issues prior to that mishap.
Scott here at the shop has accidentally got zoa slime in his mouth a few times - his lip goes numb and he has a metal taste in his mouth for a few days. Fortunately for him, that's been the extent of his malaise... after once you'd think he'd be more careful, but it's happened to him a few times.
And of course there are venoms from rabbitfishes, lionfishes, urchins, etc., that usually isn't life-threatening (except for allergic reaction), but it can put someone in a world of hurt. Accidental tagging should be dealt with by running the hottest water you can tolerate, over the wound, and it's not a bad idea to use the uninjured hand to make sure the water isn't scalding you, because the pain from the venom might mask the pain of being scalded. Heat breaks down the venom. Always good to visit the ER after a tag, just in case a spine is left in the skin.
Yep, our tanks have plenty of perils, but reasonable care and common sense should prevent any adverse affects.
Jenn