For context, "wave someone over" is your interpretation and "greet people and invite them to the table" is what OP expressed in the post. To be clear, I'm saying they don't mean the same thing and I imagine the downvoters are saying the same.
I think the community does appreciate differing opinions and interpretations--when they make sense. I don't think it's a matter of "failing to understand OP's question". Rather, I think it's a matter of failing to be convinced by an answer. Ultimately, I figure that you received downvotes because your interpretation and what OP mentioned are not the same. If I wanted to allow some room for incorrect wording by OP, then I cannot reach your conclusion. For me, there is not enough evidence to suggest that OP meant "wave someone to the table". Nowhere in the post did OP mention any kind of gesture with the hand. I do not have any experience that tells me that learners confuse "wave" and "greet" (if you do, it doesn't hurt to mention that in your answer). They seem distinct enough that a typical learner would not confuse them. It's possible they really meant "wave", but I cannot determine that with what's given. Therefore, I would side with the downvotes. But that's just me.
I can understand trying to guess what OP's intended meaning is. But be clear about it. Say somewhere that you think OP really means what you wrote instead of what OP wrote. Furthermore, instead of assuming you have the correct interpretation--instead of guessing at all--why not ask OP what they meant?
- What do you mean by "greet"? Do you mean a kind of gesture with the hand?
- Can you clarify the situation? What's the context? What is happening?
Or request whatever clarification it is that you want. Sure, sometimes readers, regardless of their background, misunderstand the question. But that's why we have the ability to ask for clarification. That's also why we insist that askers provide plenty of context. That way, everyone's on the same page, and OP receives an accurate answer that is verifiable.
Regarding the "accepted answer", it does not always mean your interpretation was right. The check mark could mean any number of things from "this completely answered my question", to "I thought I wanted X, but your Y seems better", to "eh, I don't really care, this seems good enough". Sometimes, it could be the case that OP mistakenly believes that an incorrect answer correctly answered their question. So, there's the possibility that your interpretation was wrong, but OP thought it was better. There's also the slim chance that you've convinced OP that the two phrasings are equivalent.
As for votes not being reversed in a timely manner, well, that's just how it plays out. It could take several hours, or even days, for your net votes to become positive, or for a downvoter to retract or reverse their vote. Downvoters might forgot to revisit the question and answers all together. That's just how it is. In general, you can't expect reversals to happen within a couple of hours (from the time you edited to the time you posted here). If it's deserved, give it some more time.