The saying was at least trying to claim something different. The claim was, more or less, that democracy/capitalism (people making this claim didn't distinguish them, mostly) brings peace through freedom and prosperity.

It was more a claim about Western European countries, which, propaganda aside, were not puppet-states of the US.

Cold-war era US puppet-states were different, and at the time mostly didn't tend to have Macdonald's, at least outside of a capitol. We were busy subverting their democracies, and civil unrest doesn't go well with Big Macs.