Talfuchre, from what I understand, Dalton's atomic theory was the attempt at explaining fixed ratios, and from that theory, he came up with the Law of Multiple Proportions (multiple fixed ratios) like you put above.
However, when Dalton stated "When atoms combine in only one ratio, '..it must be presumed to be a binary one, unless some cause appear to the contrary'." that was his 'rule of greatest simplicity', which was different from the LoMP. Dalton assumed that if two elements bond to form a compound, then assume that the ratio between the two element atoms is one to one, because that's the 'simplest' combination there is. Of course this is wrong as proven by modern science, but that was Dalton's assumption, and he knew it wasn't necessarily correct.