My chemistry is too outdated and limited to really break down an answer but it occurred to me to dig about as to what is in molasses.
If you 'chemical composition of molasses' and view the images then there is a legion of charts some of which show a significant difference between cane and beet molasses. This link for instance shows a signiicant difference with pH with their sample of cane molasses at ph5 and signiicantly that sample also has a substantial level of reducing sugars. The old school biology test for glucose will precipitate copper salts from benedicts solution for instance.
This link which happens to be beet molassses also gives an indication of the variety of minerals within the complex (not really a suprise since we're looking at organic life).
So….(and this is a simpliied 'stretch'
.. it's seems reasonable to assume that cane molasses would have enough acidity to break down some of the iron oxides into a soluble form as well as perhaps some indirect reduction. (perhaps the complex of chemical composition having an effect analagous to a catalyst?). It may/my not be that the effect is more pronounced on the oxide than crystalline iron (and anyway the reaction is slow enough that users stop when the rust has gone. A test with leavng a piece of clean iron for months?).
Because of the complex of organic compounds there may well be a binding effect on free iron to other compounds conveniently called chelation here.
I other words everyone is correct (or the soup of molasses is too complex to unravel)
pgk