Most people recognize motor oils by their multi viscosity rating. Viscosity refers to the thickness, or flowabiltiy of an oil. Generally, thicker oil means higher viscosity and better protection at higher temperatures, and thinner oil means lower viscosity and better protection at lower temperatures (especially at startup).
The "multi" in "multi viscosity" refers to an oil engineered to flow at the lower viscosity rating (eg.the 5 in 5w30) when cold, but perform at the higher viscosity rating (the 30 in 5w30) when hot. The "w" indicates that the oil is suitable for winter use.
Synthetic lubricants posess a host of improvements over petroleum based lubricants, with little to no drawbacks other than higher cost. Synthetics provide a much more effective protection within a wider range of temperatures, and do not break down as fast as petroleum based oils. Synthetic oils are laboratory produced at a molecular level, so that they contain only what they are meant to contain, with no contaminants. Petroleum based lubricants are derived from crude oil, and even though they are highly refined, they will always contain significant amounts of contaminants. For this reason, just adding a synthetic additive to petroleum based oil will not have the same effects as using a full synthetic.
There are basically only two situations when synthetic oils should not be used in an engine. The first is on a brand new or just re-built engine. Synthetics provide such a high degree of wear protection that they will not allow a new engine to properly break-in. Synthetics can be used on new or re-built engines after the break-in period. The second situation is when an engine already leaks or consumes a significant amount of oil. This is due to the high cost of constantly replacing the oil and the fact that an engine in this state of tune may need to be repaired or re-built anyway.
I have not seen any documented proof that proves without a doubt that synthetic oils do no harm (or good) when used during the break-in period.
Mobil 1 states that "Current engine manufacturing technology does not require this break-in period." They are saying that modern engines do not require a break-in period, not that synthetics shouldn't be used during a break-in period. Their statements leave a bit of a loophole for the lawyers to sneak through.
The only facts I have are that some synthetic oil manufacturers instruct against using their products during break-in, some owner's manuals and vehicle manufacturers state the same, and many engine builders and mechanics also make this same recommendation.
Your statements are true - there is no documented proof, and it may well be an urban myth when all is said and done. However, it seems that many people more educated than myself support the myth, and since going through break-in with conventional oils should realistically do NO harm to an engine, but going through break-in with synthetics MAY do harm, I would (and did) personally err on the side of popular convention.
With your inquiry in mind, I plan to change the wording on my webpage to reflect the idea that there are differing opinions on the use of synthetics during break-in, and that "do not use it" is not truly the gospel, as is currently stated there.
I attempt to keep my webpage as helpful, up to date, and technically correct as I possibly can, and feedback like yours aids in achieving this goal. My page will be better for it.
Important Note on Synthetic Manual Tranmission Oil:
In other words, if you are going to use motor oil, use conventional, not synthetic. If you are going to use manual transmission lubricant, you can use synthetic safely.