I also would not expect a milky/oily Strong Blue to be sold by Tiffany's. It was also my understanding that they rarely buy and sell stones with more than faint flor, as they don't find it a valuable characteristic of a diamond, so they rarely carry stones with flor.
I had a good talk at the Infinity event I went to last night, with John Pollard and a woman who spent 6 years working for Tiffany in the grading lab AND as a sales manager who now works for another company in the industry, and both said they are somewhere in accuracy between GIA/AGS and EGL-USA. Not as strict as the former, but not as "loose" as the latter, and that it varied wildly with the grader as to how strict they were. She said that sometimes Tiffany will regrade a diamond they don't like the grade on from the former, sometimes they think it's lower than GIA, sometimes they thought it should be higher. Some stones will come with both lab reports, the original and the Tiffany. Grading across the board is subjective: even GIA uses a specific minimum baseline for each grade and a lot of things can fall into that grade. We also discussed the various labs that are considered "majors" and how strict they were. GIA/AGS are kind of inbred, but GIA is considered the standard, AGS is less strict than GIA but is still quite strict. The strictest there is out there is IGI-Hong Kong (IGI anywhere else is a JOKE). They are even more stringent than GIA. EGL USA is a little lower than GIA/AGS but EGL itself is a joke also.
This topic was discussed because of people thinking diamonds are investments and that with the constant increasing in demand and pricing relative to supply and mining, people expect that they'll make a killing on a diamond when they go to resell it and they are disappointed very often. We discussed how long it will take to get a solid return on the investment if later planning to resell, if you don't buy a diamond now of the finest possible cut and specs, it will take longer to reap any benefit when you want to resell or your kids or whoever resells, and the lower the quality/cut caliber now, the less of a percentage you will earn in the end, and if the grading report is from a less strict lab, that percentage goes down more. Softer grading has a lower ROI than accurate and reliable "industry standards". We're talking selling it later like 50 years later, not in a few years.
I know a lot of you think I constantly bang on Tiffany, and frankly, I do, I also think it's mostly quite justified. I come from a different perspective on it, and I disagree with a lot of the way they operate. But where they excel is simply in marketing, and making women especially feel they're getting a special piece. You can generally assume what you buy there is of excellent quality, and although it might not always be the most ideal cut standards there are, it's still beautiful and of fine make.
I have the cleaning kit at home from Tiffany but it doesn't do the same job. 
