Joshua,
This is somewhat a loaded question, but I will give it a shot. Note there will likely be a LOT of comments and opinions on this issue! I needed some additional time to think about the best way to try and answer your question.
I run synthetic in all my cars and typically change my oil between 5k-7k miles depending on the oil and the car.
I have a GMC truck, 2 BMW's and the VW at the moment.
There are a LOT of factors that play into how and when I change my oil and how and when you should change your oil. Some people get overly scientific about it and perform used oil analysis to help determine when to change their oil, however, most only perform the oil analysis once the oil has been drained during an oil change. To perform the oil analysis properly and use to this determine your oil change timing, you perform multiple oil analysis and use the oil analysis information to determine the time to change your oil. The problem is oil analysis is expensive and it is not cost effective to do this for cars that hold between 5-7 quarts of oil.
Mileage cannot really be a good indicator of when oil should be changed, you really should determine oil changes based upon the total number of engine revolutions, along with other factors of temperatures and driving conditions. This is really a hard thing to track and determine.
Additionally the driving conditions, engine load and engine, fuel delivery and ignition system health play into oil condition and contamination.
For example on my BMW's they recommend 15k mile oil change intervals. There is some give and take this this figure as BMW actually tracks the fuel usage to trigger the oil change indicator. This is close to tracking the engine revolutions, but there is a BIG difference on the amount of fuel consumed while idling and during wide open throttle. Note that BMW's tend to have rather larger crankcases, typically 7 quarts of oil, run full synthetic oil and if you use the specially formulated oil, it can and will run up to 15k miles without significant engine wear.
Many other things play into oil change requirements such as the time of year, the length of trips, the amount of traffic you sit in and so on.
You also have to realize that economics and time plays into the oil change intervals as well. I have 1 car that has about $100 worth of oil in it, so I am not likely to change this oil every 3000 miles. Other cars have close to $50 worth of oil in them. Also with 4 cars to keep track of, I do not have enough spare time with cooperating weather to change oil every weekend of the year.
On major thing that can impact the oil health is short drives in the Winter time where the oil does not warm up enough to cook off water vapor. This tends to be more true the larger the oil sump is and what the outdoor temps happen to be. Engine coolant comes up to temperature at least twice as fast as the engine oil temperature. If you ever check under you oil fill cap and see yellow/brown goo in the Winter time, you need to take your car on longer drives during the Winter months.
I also check my engine oil and watch the oil color and smell closely as well. It is not a full blown oil analysis, but it my way of also determining when I may need to change my oil.
As for your friend that happens to change his oil every 3k miles or so in his 10 year old car that has 190,000 miles on it only using Dino oil, this is good, likely he does not live in extreme temperature environment nor does this car drive is congested traffic. I am lucky to get much more than 10k miles on some of my cars per year, however, my engine likely turns as many or more revolutions than the engine that runs close to 19k miles per year! Additionally I deal with probably far more start/stop and warm up cycles than the 19k mile per year car as well.
So I feel the synthetic oil benefits my driving style and engine operating conditions that Dino oil and it will likely give me a longer oil change interval while still keeping the engine clean and well lubricated. Also the added heat from the turbo will break down Dino oil much faster and cause more coking , ash and varnish build up as compared with synthetic oils.
Hope this answers your question.
, the main problem is that the oil was recently changed, with no problems prior to the oil change, and now it constantly smokes. Its not making any weird engine noises. it is using oil now, so is there a possibility of a screen or oil return line being plugged up from the old oil? any help would be greatly appreciated 
