Indeed. As many have said, the RAC man has basically given you a guess. Unless he did a roadside compression test and other diagnostics, he cannot tell if the engine is goosed or not.
Yes, the K-Series (which is actually a good engine) does have a reputation for head gasket failure, but so do lots of other engines and in most cases it comes about by poor maintenance or a sudden loss of coolant (which you have had, but is not always terminal).
The cheap and easy test is to refill the engine (I would actually use proper coolant rather than water as it is not * that * expensive, and if the engine is OK it saves you having to do it again - but water is OK if cost is an issue), and see what happens.
The only fly in the ointment is the damage you mention to something which has melted. We need to understand what that is in order to advise you. Any chance of a picture?
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