Nah, Webster really did drop the ‘u’ and changed a lot of spelling. He also learned a lot of languages since back then there were many, many different languages/dialects in America at the time and he wanted to make it easier as he changed spellings, such as swapping ‘re’ to ‘er’ for phonetics. There was also a lot of anti-British sentiment at the time of course which certainly would have motivated acceptance.
Webster is definitely also credited for this in histories and not newspapers outside of anecdotes.
If we’re doing Wikipedia as the sole citation then:
https://en.wikipedia.org/wiki/Noah_Webster#Blue-backed_speller
Furthermore your quote doesn’t actually have a relevant citation:
Though in context of the previous paragraph seems to imply that this was an opinion that the wikipedia article came to simply because there was a previous work that argued specifically for ‘or’ in place of ‘our’ but again, it appears to simply be their opinion based on an assumption.