How are very long component lifetime claims ascertained/evaluated?
One of the methods is, probably as you've predicted, that of accelerated aging. This is used when the lifespan of a product is such that it would be impractical to run a normal lifespan test (such as LEDs, which have MTBFs of possibly 100,000 hours plus). Here, one stresses the test item past what it will ever receive "in the field" to achieve a shortened lifespan, from which the data can be extrapolated. 

A major consideration in the use of accelerated aging is the non-linear effect of operating outside of a part's recommended operating range. This can be illustrated with mechanical systems, such as running a gearbox at 45,000 rpm instead of 15,000, and extrapolating the data by three. However, suppose you're testing your lightbulb. Common sense would say that running it at twice the current would make it run half as long; however due to those non-linear effects you may find that lifetime is only 1/4th of that at the proper current because of the additional stress of the overrating. An important consideration is that the test device/subject/item should be well-characterized in both its intended and unintended operating range behavior prior to performing the test.

Because of that there are any number of studies (a LOT of them) on the various refinements to the accelerated aging tests in various fields. LEDs come to mind; photovoltaics are another.