Sure, there are qualitative arguments both ways in terms of trust. It was just a conjecture. I'm sure people have done quantitative research on this, and it probably varies by situation anyway, so it is probably not worth discussing further.
But that it is a different thing from off-site vs on-site. I can pretty much guarantee the optimal checkout process (among the universe of checkout processes) would be an integrated solution minimizing the number of steps and abrupt transitions in the overall process. Such an optimal process might include additional options for Google Checkout, PayPal, and others, i.e. third parties for those people who want that.
What it comes down to, is that for every step, there will be a drop off %. Putting checkout on your site allows for less steps. And it allows for more possibilities in look and feel, etc. That is, it allows you to move more freely around the universe of checkout processes toward the optimal process for your particular situation.
From experience, this universe of checkout processes can have vastly different outcomes in terms of sales. By the way, I worked on another site that saw an immediate increase in sales from moving off Yahoo Store to an integrated checkout, and then another big increase when the checkout process was further optimized with, among other things, upselling and coupons right in the process.
I just don't understand the want to move this off-site when you have the capability to do it on-site. I assume the main goal of this site is to sell stuff. So I would imagine that you would at least want to experiment with one of the main things involved with selling stuff, i.e. the checkout process. You could even run experiments testing off-site vs various on-site configurations. I suppose I could see a compelling argument if it took months to create something functional. But it is probably an order of magnitude shorter.