I looked at the site and it doesn't provide much info and anyway it is for kids so they keep it real simple. However, the statement that vinegar is a strong acid is not correct and definitely should not be in the discussion. Vinegar (acetic acid) is a weak acid and should never have been picked as the acid to use in the experiment because it introduces complication that aren't stated. It was probably picked because it is familiar and safe. For one thing, you would have acetates of iron formed. And suggesting this is equivalent to acid rain, is hardly true. The composition of acid rain can be complex involving sulfur and nitrogen and phosphate compounds.
All of this has nothing to do with what iron does in soil. Soil is a very complicated system and the disintegration of iron is likely to involve various biotics. Some ferric and ferrous ions are likely to be free, but they will exist in a system where exhange among various molecules may be rapid or slow. But there will certainly be acetates, nitrates/nitrites, phosphates, sulfates/sulfites and a whole host of organics.