need a sanity check. is this even possible?

in the last three months, I have gone from a fast food loving couch potato, to a PrecisionNutrition eating, 4 intense workout a week mad-man (and loving every minute of it.)

I started by just watching what I eat, using myfitnesspal. My confirmed start weight was 265, but I watched what I was eating for a couple of weeks before I really decided to commit and I would guess that I was easily over 270 (but too afraid to get on the scale).

My total weight loss to date, on a very accurate home scale and confirmed by doctors scale, is a bit over 30lbs total in a little more than 3 months. About 6 weeks ago i started to work out with a trainer 3 days a week. I can say that it really kicked my butt the first three weeks, but I kept going. I am down a little more than 15 pounds of scale weight since I have been working out with the trainer, although the first 3-4 weeks my weight loss STOPPED in spite of the intensity of my workouts and that i was better on diet than ever. I also have been doing body measurements every week since I started with the trainer, and I see that I am down by the following:
5 inches on waist
4 inches on hips.
1 inch on leg
3 inches on chest
2 inches on shoulders

I also started doing body caliper measurements and ran it through every calculator on http://www.linear-software.com/online.html from the basic 3 measurement military calculator, to the 7 site caliper tests, and they all show me at about 28-30% body fat. That leads me to the part where I am scratching my head. If I take the high end number, and compare it to the DEXA body composition I did at a local hospital, which showed me at 40%+ body fat.. That would mean that I have lost 10% body fat in about 6 weeks or so.

Is it even possible these numbers are true? If so, that means that I have lost about 15 pounds of total weight, but GAINED about 20lbs+ of muscle. I have been eating really well, following Dr. JB's diet, and training hard but that number seems so big. I can say that I see a difference and feel a difference in terms of muscle but I just wanted to check to see if I lost my mind. Lol.

We used the calipers according to the guide book, and the guide on the site above, when using multiple measurements I would go with the highest number so I do not feel I was cheating on the measurements.

I just wanted a sanity check, because that seems very dramatic for 6 weeks of work.
Historical note, not sure if it matters or not, but I was in good shape till about 6 or so years ago. I had a decent muscle mass back then, not sure if that makes any difference in the ability to re-gain muscle or if that is an urban legend.

thanks in advance for your feedback.
Mike