Our founder, Rich Johnson, taught me back in the 1990s that he thought CBC studies should include at least another (fairly unimportant) "decoy" attribute other than just brand and price. That way, respondents would be less likely to see that the study was just about brand and price. The utilities for the "decoy" attribute should be estimated, but their impact could be ignored in the market simulator (which only dealt with brand and price). This seems like good advice to me, though I think it has generally been ignored by the Sawtooth Software community.
I wish I could say that a great deal of evidence has been accumulated one way or the other (about including or not including the "decoy" attribute in CBC). But, I cannot think of a single case comparing the results with or without the decoy.
That said, if brand + price only CBC's were systematically failing because respondents knew it was just about brand vs. price tradeoffs, there would be a lot of grumbling and abandonment of this approach--which is not seen.