Incorrect book, and deeper evidence
The Easter Island theory is detailed in "Collapse", not "Guns Germs and Steel".
I don't think Jared Diamond's theory has been proved incorrect. It wasn't just made up - it was based on multiple sources of evidence, especially the pollen record in peat bogs (hard to fake and quite strong evidence). Rats were not introduced by Western ships, but came a lot earlier with Polynesian settlers, and the damage was done over centuries, not in the 19th century.
The Polynesian people had been extraordinarily successful in settling many islands across the breadth of the Pacific, and on arrival Easter Island looked very similar to the others. The climate and soil were not nearly as robust as other locations, but in the pre-Modern era it would have been very hard to establish that. The combination of slow regrowth, high usage and damage from introduced species (rats!) led to the gradual disappearance of Easter Islands forests.
The book also covers interesting parallels with the Norse settlements in Iceland and Greenland. This is similar to Easter Island, where seafarers from more robust lands arrive at islands which have centuries of forest growth looking much like previous islands. High usage of the timber exceeds the regrowth and exposes fragile soil, which erodes, leaving no chance of the forest being sustained. Greenland collapsed and Iceland came close.
Certainly the arrival of Western slavers and disease dealt the final blow to Easter Island, but the archaeological record suggests other significant events prior to that.