Of course dictionaries credit the people first known to use words with the earliest usage of that word. What possible alternative could there be in the pre-recording age? Nobody annotated their writing by saying “I didn’t coin this word, I heard Foulsham ffolkes say it in the Ye Olde Oxford Pub on May 22, 1578.”
The real question is how to know who used the word first. You can start with the OED but it is no longer a serious scholarly tool, although unquestionally valauble.
First, the OED was a volunteer endeavor. While the editors did some reading and word-collecting of their own, they relied on a network of thousands of individuals who combed through texts and listed words (in the context of their sentences) to send in.
A random group of uncoordinated volunteers will show a large number of biases, conscious and unconscious. They will prefer to read well-known, popular, or personally interesting material over obscure, dull, and forgotten works. The OED editors encouraged this subtly by pitching their dictionary as a reference to the greatest writing in the English language. Shakespeare was obviously included to the last comma, but that doesn’t mean that every contemporary was also mined for the last syllable or even included at all. Except for words used by famous writers, words with no continued usage were deliberately ignored. Additionally, because of the emphasis on great literature, non-literary works were handled with less care and diligence. Scientific words were done particularly badly, but many other word classes are also scanted. Because almost none of them were lexicographers, the volunteers had no idea what to look for and what to exclude.
Availability was also a key factor. Printed works were preferred. This is part of looking at the literary heritage of the country but also a reality manifested by the physical difficulty of doing research in the 19th century into letters, diaries, privately-printed tomes, and other ephemera.
It gets worse. The dictionary was printed in multiple volumes in alphabetical order over 40 years. Once a volume was printed it was fixed. The cost and physical difficulty of setting up and printing such unique pages were prohibitive. They learned from their mistakes and the later volumes show many differences from the first, but vol. 1 is from 1888.
The dictionary was constantly underfunded and yet a huge money sink for the Oxford University Press, which was never prosperous and always had many other scholarly projects to fund. The staff lived in genteel poverty and worked in conditions a Dickensian clerk would recognize. Any corrections that came in to a finished volume would be literally pigeonholed. Forgotten material was still being found decades later.
The OED that people are familiar with, and that includes the compact OED with the magnifying glass that far more people in the U.S. have because it was a cheap lure to get people to join book clubs (that’s where mine came from) is still the first edition. There is a second edition, finally published in 1989. That did not start out computerized, and it faced the usual budgetary constraints. The editors had to decide whether to correct the literally hundreds of thousands of mistakes of all sorts in the text or add the tens of thousands of words missed or added to the vocabulary since the first edition was fixed. In the end they did some of both and pleased almost nobody.
The third edition is entirely computerized and will attempt to correct everything and add everything and stay roughly current. It will be out sometime after I die.
Shakespeare was prodigiously prolific and did have a vocabulary that was amazingly large. He did write in a time of ferment. Many of the words he is credited with coining, though, are variants in meaning or part of speech on already existing words rather than truly new words. And modern scholarship keeps finding older uses of many of these supposed coinages. Even the OP’s link cites only 1700 instead of 2000 and that’s probably down to 1500 today. It will be lower in the future.
Did Shakespeare invent many words? Undoubtedly. Anybody at the time interested in word play to begin with and needing to bend and shape words to meter, internal ryhme, assonance, alliteration, and all the other tricks of declaimed speech to fill out a play would naturally add as many words as possible. Everyone in the era did so to some extent. Shakespeare’s popularity made many of these coinages familiar through repetition and imitation. But the willingness to be free and open with words is what makes him popular in the first place. Coinages are a secondary effect of his overall ability, which is to write words that people keep wanting to hear.
Is that anything that anybody says about de Vere?
Wiki says “The estimated date of completion is 2037”!