A large number of homes built here in North and West Vancouver ( all area's actually) from 1980 back have been painted with some oil paint. Baseboards, doors, window sills, bathrooms and garage entrances as an example are the normal areas where they used oil paint. This is actually a good thing (providing it is lead free of course) because in my opinion oil paint is a smoother and more durable finish for those areas.  However, in my experience I have seen a lot of painters or people paint latex paint directly over  oil paint with no knowledge or "remorse" for the client or job preparation.  If you have ever noticed painted areas that scratch easily, it is most likely because the surface wasn't scuffed and or re primed for the latex to adhere to the old oil finish. It takes time to do things right so don't be fooled by a cheap and fast quote. People paint over many things without even checking if its oil or latex.  There is a shortage of "professional painters" out there.  I've worked for companies that don't care about doing things right.  It's all about the money.

• Two ways to deal with this.  Paint oil with oil again or re prime with an alkyd paint and then you can go over it with a quality latex.  I personally feel base boards, window sills , door casing and definitely interior exterior steel doors look better and last much longer when painted in oil paint.  Oil doesn't scrape off  as easily from keys in hand, vacuum cleaning along baseboards, dogs scratching on doors etc.