I think it's right to be concerned about the possibility of mindless close voting, but I think this is not only a danger in chat - in fact it may be less of a danger there than in the queue. I also don't see any reason why moderation activity should be confined to the queues, or practised without collaboration, or left to itself.
To elaborate on the first point, I would hope that anyone who sees a suggestion to take an action on a post will read the post and decide whether they agree with the suggested action. Let everyone be reminded to do that always and without fail ;) In practise, we might sometimes, as you say, believe Experienced User that this question should be closed as a dupe or whatever and just click the buttons. Personally though I think that's less bad (actually I feel inclined to trust certain people's judgement) than voting to close in the queue on the basis that three or four people have already voted, so their judgement must be right - they might all have been as clueless as me!
I'd say it's a responsibility of the person suggesting moderation actions in chat to be sure they are suggesting a correct action, and also to be aware of their audience (are there any new users or new close voters in chat today?). More helpfully, they can give an explanation if one is needed. Users who see such suggestions and disagree with them should certainly challenge the suggester to provide an explanation, or explain why they disagree with the suggestion.
Giving an explanation makes the act of suggesting much more useful because it provides an opportunity for people to learn how to do moderation. I'm not talking only about close voting, but about up and down voting, flagging, commenting, editing. It's much easier to learn how and when to do these things, to pick up an understanding of scope and policy, with the opportunity to discuss them with other users. It's hard to learn them in the queues alone.
The opportunity for learning is one reason I feel raising moderation issues in chat shouldn't be discouraged. But since many people aren't very interested in doing that kind of activity (probably they are answering questions which is of course essential - it's like the paid work of the household, while moderation is like housework) I like to hang out in a room only for moderation where we are always asking for votes and other actions, not primarily for learning purposes (that happens incidentally) but because we know that correct close (and reopen) votes often age away without an extra push, especially when the close votes queue is full or during the summer holidays or whatever, purely because there are too few active reviewers at the time. Very often there are less than 5 active reviewers of close votes, and (I'm saying this as someone who loves to hit the back button when reviewing to see who else voted and how) reviewers are often not unanimous.
My mum and I joke that housework is done by fairies, because folks express amazement over its not having been done when the houseworkers were otherwise occupied or indisposed. Moderation will not do itself, and certainly not if it's confined to review queues or never talked about. We should be able to use all available channels and tools to help each other to do it. Why not? It's not really like asking for an upvote, which is bad etiquette because upvotes only benefit the receiver (in fact there are occasions when asking for an upvote is a moderation suggestion and perfectly acceptable - when making OP's self-answer-in-comments into a community wiki answer to have the question show up to visitors (and the system) as answered). There's IMHO no reason why we shouldn't talk about such matters in chat, though maybe we should do so with explanations rather than only saying "this needs one more vote".