Mr WordyDifferent people have different opinions on this, so you pays your money and you takes your choice I guess. Here are a few (randomly Googled) definitions that agree with my position:
Yes, of course. I wasn't even saying you were wrong. I just found a definition in a dictionary that is fairly descriptive in its views and consequently it records actual usage, unlike prescriptive usage experts. Personally, I have no strong opinions either way. The fact remains, though, that 'alternate' is very often used to mean 'alternative'.
My liberal and descriptive attitude towards grammar and usage may have something to do with my studying the history of the English language. The only unchanging thing about it has been change. The grammar has changed, the vocabulary has changed, the pronunciation has changed and the meanings of words have changed - and will keep changing. Nice derives from Latin nescius, which means 'ignorant' but very few people object to its modern meanings even though every one of them was grossly incorrect when first used. Once a word has been used incorrectly for long enough by enough people, it becomes standard English.
People usually have nothing against changes that have happened before they were born but many object vehemently to changes that are taking place in their lifetime. That is human nature. It happens in all languages. It is a common belief that changes that are happening right now somehow seem to be spoiling the language.
CB