There's a better than average chance that your first job is going to be with a CMG. New grads are a distinct gamble (see any of the numerous posts on what residency teaches vs. what is required for success in the community). Many independent groups (especially in desirable areas) don't need to risk that gamble.
Every group regardless of size has certain things that must be done in order to service the contract. The group has to bill patients, attend administrative meetings to keep C-suite and the med staff happy, and perform QA on their docs. There are definitely other tasks that I'm forgetting, but failing to do any of those things consistently will result in losing the contract.
All of those things require overhead (you could argue about the admin stuff but not having a shift buy-down or compensation for meetings is inherently unstable) and that overhead is going to come out of the group's collections. CMGs always have an additional overhead component which is going to be shareholder profits. Many non-CMG groups are also going to have something equivalent in terms of increased payments to the contract holder (non-democratic) or contract holders (democratic with distinction between partners and non-partners).
In markets where there isn't much competition, CMGs can depress pay to increase shareholder profit and still keep their contracts. This tactic is also available to the other types of groups except for democratic groups that don't have non-partner MDs. In markets where there is competition, CMGs offering below market pay are going to hemorrhage their docs to better paying places. Their replacements, crappy or brand new docs, can't keep metrics at the level needed to maintain the contract. At risk of losing the contract, the CMG starts offering competitive pay to get quality docs. The various CMGs can't collude with each other because of anti-trust regulations, so this effect works even in markets dominated by CMGs as long as there are multiple CMGs in the market.
Now where things get interesting is that the core functions for maintaining a group are constantly increasing in cost. At some point, the economies of scale for CMGs in terms of billing, CME, core measure reporting, etc. are going to largely offset the profit that gets skimmed off by the shareholders. In some markets this is laughably far in the future, in others (Houston for one) the pay between CMG and non-CMG groups is roughly similar.