Ok, I said I would post back after reading the articles. I have looked at the articles and can now add the arm-waving with a bit more confidence. Well, I've looked at MOST of the articles anyway. The Internet is being a punk so I haven't looked at all the pro-garlic ones. Looked to me like the pro-garlic articles were mainly concerned with freshwater environments and possibley non-fishy environments though, so I question the relevance of those to marine tanks.
Regarding the heart/liver-related articles cited by Wombat (presumably Dr. Bricknell), they concern three plant extracts: rapeseed oil, lineseed oil, and olive oil. Basically what I get from those articles is that it's a bad idea to raise or maintain your fish using those as a staple diet or large component of a staple diet. The studies do report liver and heart complications in the fish, but one also reports no such illness (although it does report other effects, such as decreased growth rate). The statement about marine fish lacking a certain enzyme present in freshwater fish is supported by some of the articles (two enzymes actually), and this has to do with production of fatty acids. The mechanism one article seemed to be putting forward was that if you screw up the fatty acid levels via a bad diet, you get liver and heart problems. That all seems reasonable to me. However, I am not seeing a direct tie to garlic as an addative from any of those articles. These articles are using the plant extracts as a primary diet or a large percentage of a mixed diet (such as 50/50 with fish meal). As far as I'm aware, nobody is using garlic that way, although I don't know by weight how much garlic oil you'd end up with from soaking something like flakes. There are some chemical breakdowns of what all was in the tested oils, but nothing jumped out to me as something to go hunting after as a connection to garlic specifically. If anyone would like to go on that hunt and can't get a hold of the articles for whatever reason (I did have to get them through my university library), I can PM or post the tables.
This doesn't mean that there is nothing behind Wombat's statements, just that I don't see an obvious generalization from those articles to what he was saying. I don't see any resolution to the issue one way or the other from the cited materials. Similar to what StandbySetting said, until I run accross some more relevant articles (maybe they exist, I have no idea), garlic will still be in the category of aquarium voodoo for me.