I can't be bothered to look up the correct legal wording but if you think about it:
1. We would probably all agree that any oil installation must (by law) be fitted to building regulations and manufacturers instructions.
2. All manufacturers instructions I have seen for oil boilers state clearly that the appliance must be commissioned by a 'competent burner mechanic' (or similar wording). Also oil pressure/combustion must be set up.
3. To prove you are competent it is generally accepted that a person must have completed training and exams on an industry approved and recognised course. Just saying you are competent or reading a book in not good enough.
4. As you say a person would then have to buy gauges and an analyser and as we know they are not something a DIYer can just use out of the box therefore training would be required to know how to use them correctly.
So although unlike gas there is no law that says you must be qualified to work on oil appliances, by the reasoning above it could be said that is is not possible for a person to legally set up an oil burner unless they have at least passed a course such as OFT101.
Let's say a chap tries to service his oil boiler that we know is producing high carbon monoxide indicated by the soot, and through lack of knowledge/training/qualifications does not notice something dangerous that a qualified engineer would, or does something to make it worse, and either by chance or incompetence the next day that boiler catches fire or produces so much CO that someone dies.
The man is left with that on his conscience, house insurance refusing to pay up, a dead relative, a court case and a prison sentence, all because his ignorance/stupidity driven by a desire to save £100 by not paying an engineer do do the job correctly.
As professionals and the face of a safety related industry we should all give a united front in only ever advising people to use qualified persons to do work even if the law does not say so. In doing so we may have a little more work and as the years go on get rid of all the poor/unsafe installations we see every day and maybe save a few lives and alot of unhappy homeowners. How many times have we all been to jobs that have obviously been attacked by a DIYer, made worse and cost them more to correct it than to have had it done properly the first time.