That's not the point. Any composer, or arranger, can plug in any harmonies he/she/it wants into a series of pitches. Some of the greatest jazz improvisers excelled at just that sort of thing - it's part of their genius.
My basic kindergarden rudiments of music point [this is the kind of thing beginning students learn and figure out right away] is that given a series of pitches, the harmony is implicit - short of some really radicalist expirement, or some Asia or African folk idioms.
To make the [kindergarden] point even clearer, consider the following series:
C D E G E D
That's a nice little melodic fragment. What's the harmony? Is there harmony? According to most of the untrained posting here, there isn't - due to their complete lack of music knowledge.
But, in fact, the harmony of that little melody is very clear. It's pure C major.
To address your remark - "A melody can be harmonised in many ways" - sure. We may take this very melody and do all kind of things to it and with it, INCLUDING dissonant chords, dissonant counterpoint, etc. etc. etc.
For those of you who still don't see it, and still don't understand - you won't understand music theory [keeping in mind that the points here are, again, elementary kindergarden stuff]. I strongly suggest the following for most of you:
1. Listen to music and enjoy it without worrying about technical points
2. Don't reach conclusions about music based on ignorance and lack of training - and worse - carry those erroneous conclusions around with you all of your life - and still worse - allow your erroneous conclusions to infect the way you relate to music.