Whether we're talking literally about a secret sauce (such as with the McInhenny Co. and their Tabasco sauce) or using the term to refer to a particular technical specialty or core competency, most of the companies that have survived for over 100 years attribute their success to the accumulation over time of some specialized knowledge and skills. They believe these company "secrets" or special methodologies make their organization unique and not only differentiate them from the competition, but make it difficult for others to imitate, thus giving them a sustainable competitive advantage.
The belief held by the old companies that their products or services were difficult to copy and that their offerings had a strong appeal other than price wasn't significantly different that that of many younger firms. However, the old firms were more likely to indicate that they build on their unique characteristics in every aspect of their business - into the fine details of their offering, how they train and educate new employees, how they work with suppliers, and how they convey this uniqueness to customers as part of the sales process.
Another area where management of core strengths was unique among the older companies was how they build on their strengths over time. They report having some things that do not change in product quality, raw and processed materials, and production and sales methodologies; but they also report constantly working to improve their operations and develop their core competencies, even in the best of times.
Members of the "corporate century club" know they are special, and not just because they have managed to survive world wars, economic depression, huge advances in technology, globalization, and major shifts in social and cultural preferences: they know what is unique in their DNA and they cherish, protect, and build upon it.