White box to me from them means refurbished. The warranty is most likely through them. Not sure the pricing but if shipping is free and its $100 or less, then I'd buy it. I won't buy the gray market becaus they weren't meant fr sale in the US. I don't want to have warranty problems down the road, or even repair issues.
As to buying here, it can be an option. Many people here offer good deals on lenses, however I have found far too many want far too much for a lens. In some (many, actually) cases, the pricing for a used lens, after shipping, would be so close to new price you won't even save 10% and you wouldn't have a warranty. -As an example, a new 50mm 1.4 goes for $369 to your door and I normally see people here wanting $340 plus for a used lens without a hood or anything else, and they may want shipping or fees on top of that price.
For example, on Amazon the lens new is $110 shipped. Used ones start at $100 shipped, so why buy used when you don't get any type of warranty? In fact, after looking at the Adorama site, I'd just buy from Amazon, though you may wait a day or two extra for shipping.
*edit... I should note that I bought my T3i kit through Adorama a couple months back as a Canon refurb unit. Cam with a 1 year warranty and everything in the box. Was $600 vs $750 new and when I came here, I found people were asking over $600 for their T3i kits, or close to $600 for the body only. I wouldn't hesitate to do business with them again, and most likely will.