I don't know for sure if you were lied to; some people just don't know better or care. I have been driving Buicks (with the same basic engine you have) since before your car was new. I have been using synthetic oil in my engines (probably) since before you were born. Amsoil (a synthetic oil manufacturer) was first marketed in (I think) about 1972.
https://en.wikipedia.org/wiki/Amsoil Oh, and my cars leak nothing. My college aged son will tell you I'm OCD about spots on the concrete driveway.
Synthetic oil offers several advantages over conventional oil; Synthetic oil is used as a substitute for lubricant refined from petroleum when operating in extremes of temperature, because, in general, it provides superior mechanical and chemical properties to those found in traditional mineral oils.
https://en.wikipedia.org/wiki/Synthetic_oil
Among the advantages to synthetic oil is its longevity. Mobil1, Valvoline, Pennzoil, Castrol and other manufacturers of synthetic oil make oils that are designed to go 10-15K without changing the oil. I run Amsoil 5W30 synthetic in my wife's 2004 Buick Lesabre (with the same basic engine as your Park Avenue Ultra); I'm also running bypass oil filtration and doing used oil analysis, but I have 20K on the oil in her car and test lab report showing it is "suitable for continued use."
The "leakage" issue with synthetic oil comes from its superior lubricating and detergent qualities. Some older engines which may have been run on conventional oil for awhile may have accumulated sludge and varnish and have some stiff older seals. Drivers switching to synthetic on "high mileage" (over 75-100K) may have synthetic oil clean their engine to the point that these seals start leaking. But technology has given us a solution: ATP-205 reseal will condition and many times soften these seals and stop leaks. http://www.ebay.com/itm/ATP-AT-205-Re-Seal-Stops-Leaks-8-Ounce-Bottle-New-Free-Shipping-/361284259916?hash=item541e38504c:g:TicAAOSwrklVOECS
The 1993 Buick Park Avenue Ultra came factory stock with a series I supercharged engine.
https://en.wikipedia.org/wiki/Buick_V6_engine Notice the engines in the cars I drive are just a little further down the page than yours. This engine, in my opinion (and that of many others) is one of the best engines GM ever made. It has an all steel timing chain and gear set, excellent oil pressure, famously strong internal components, and the series II and III versions have an extensive array of aftermarket parts available used for racing:
http://intense-racing.com/Merchant2/merchant.mvc?Screen=cp-innovations
Oh, yeah,