Making beer is all about controlling variables: quality of ingredients, temperature, sanitation, etc. Using ice to chill is obviously a method employed by many people, and with success. The two problems that I see are 1) contamination (which has already been extensively covered), and 2) the inability to do a full boil, which is important to me. I just use an entry-level copper wort chiller, and am fortunate enough to have 55F well water to do the chilling.
I was invited over to a brew session by an acquaintance, and he & his brew buddy use ice to cool partial boils. At that time, they were having no trouble. Suddenly, within the last few months, they've thrown out three batches. They haven't found the cause yet, but given my observation of their techniques, there are several things they need to eliminate as possible causes, and the ice chilling is one.
The issue of contaminated beer by your friends certainly merits investigation. To confirm if it is the ice, a simple culture test of the water source would be in order or changing to purified bottled water would probably work. I am inclined to bet that it isn't the water, however. The reason I say this is because the water would have to have a high number of contaminants to infect a batch of beer. I tend to think that a ratio that high would probably make someone ill if they drank it. BUT, it is very possible the ice is the culprit. Testing the water would be a step toward discovery.
I am just afraid that if you take away the ice, you may automatically assume it was the ice. And you may not find the actual culprit. I would lean toward equipment contamination and overall technique first. If you can't see mold growing in the wort, then I would assume either a Bret. or L. Bacillus infection.
I have not been reading the "no-chill" method used primarily in Australia. I will have to do that.