The cardinal rule of interacting with advisors is that if you don't generally trust your advisor's advice, then you need a new advisor. So you should start with the idea that your advisor's approach to any given situation is probably worth trying, and only give up on it if it's clearly not working out or seems contrary to what everyone else is saying.
Beyond that, I'm sure it varies between fields. I wouldn't presume to offer advice to someone in a biology lab on how to sort this issue out, for example.
The most important thing, which you absolutely must do no matter what, is to inform your advisor in detail of any help you receive. This is a matter of intellectual honesty, while everything else is a matter of convention or wise strategy.
What you want to avoid is the following scenario: you meet with X, then meet with Y and explain what X said, then meet with X and convey Y's response to X's ideas, then meet with Y again and relay information back from X, etc. If you try this and are a little vague about the line between your own ideas and what you learned in your last meeting, then you can pull it off for a while, but eventually you'll be in big trouble when X and Y talk. Even if you never actually lied, but just let people assume you were contributing more than you actually did, they'll be very unhappy if they decide you weren't contributing enough. [And this can be a particular danger for students: if someone says something cryptic and then you figure it out later, is that because you are adding new ideas and insights, or because you are catching up to where the expert already was? It can be hard for a beginner to judge, and this potential for confusion is a valid worry for advisors.]
As to how to introduce the idea to an advisor who resists getting outside help, the main thing is to understand why. Is it because your advisor feels this is an important learning experience for you? Is the advisor convinced that the problem is not as difficult as you fear? (And, if so, can you make a compelling case that it is?) There are also more worrisome scenarios. For example, maybe the local expert in this area is notorious for competing with or undermining students, or has a bad relationship with your advisor. Your advisor may be reluctant to say this explicitly, so if he/she seems to be ruling out a natural collaborator for unclear reasons, then you should ask about other people you might talk with instead.