I think giving control over the group in a large way to the player might be the way to go. No, the player's character isn't the leader of the group, but, the group now becomes a player resource to be leveraged in the game. Same as having a cool magic item or anything else. The player gets to tell you what the thieves guild is doing, rather than the other way around.
Well, what is the *purpose* of having them engage with an organization?
If the purpose was imply to give the player more resources to work with, a tool to use in a larger venue, then what you suggest is fine. The organization, in a sense, becomes a big old magic item the character possesses and can control.
If the purpose is to provide hooks for NPC interactions, motivations and events that would generally become plot twists in the resulting narrative... this solution isn't so hot. If the organization generally does what the player wants, there isn't any need for interaction with the NPCs in the organization, and it isn't a source of narrative complication or tension, any more than the fighter's sword is. I mean, there's a complication when the sword fails to do damage, tension when someone threatens to Sunder it, but not a whole lot else.
The issue is that the vagabond wants to go through life without complication, and the typical purpose of the organization is to add complication.
There are two basic reasons I can think of (already mentioned, but let's remember the) for the player wanting to avoid complication:
1) The player fears a hidden cost. Maybe they have been bitten in the past, where the complication was overdone, so that the player did not have a good time. This is a trust issue. For players who like manipulating rules, laying out the rewards and costs of being in the organization, codifying them, sometimes can help with this. For those who aren't big rules monkeys, or who don't trust you to stick to your own rules, no amount of rules will make them comfortable - the trust has to be built in other ways.
2) The player over-values their freedom. A real-world example of this is a person balking at a good deal on a cell phone contract, because it has a two-year commitment. In reality, very few people change their carriers frequently. If you didn't have the commitment, you'd not change anyway, so being committed really isn't an issue. In a sense, this is a variation of (1) - but the cost is an opportunity cost, specifically - the fear that making a commitment now will preclude them from greater rewards later.
The way through (1) can be a real pain, as building trust is hard.
(2), however, is easier. You handle it in the same way as a cell phone company handles it - override the fear of opportunity cost with current opportunity and features! Find something the player wants. Make organizations the best way to get it. Make your organizations into bright and shiny cell phones that folks stand in line to be part of. This, unfortunately, doesn't lend itself to general organization rules - it is too dependent upon the particular player and character, to it is more a campaign or adventure design consideration.