It is difficult to see how one can have "strong product brands" and yet not have a "strong corporate brand". Similarly, a "strong corporate brand" must be kept up by strong products. A reputation for quality and innovativeness as well as for corporate social responsibility (especially when one is talking of things like care for the environment) must ultimately accrue from the performance of a company's products and services in the market place. On the other hand, as a matter of brand management strategy, emphasis on building a strong corporate brand without a concomitant emphasis on building strong product brands is unlikely to be successful.
For entities like resellers, this is still true - while the strength of the product brand is derived, the service which is the core offering of the reseller still needs to be built.
My experience is largely in IT services so naturally my focus has been on building strong corporate brands.
However, I do see the merit in building strong product brands. A recent example is Bajaj in India. The conglomerate is into financial services, motorcycles, electrical appliances etc and now wants to build strong product brands to differentiate its businesses, specially in its motorcycle business.
But my guess is that even in such cases, companies will see merit in consolidating brands by lines of business at some stage. After all, regardless of whether you buy a Camry, a Corolla or an Innova (all Indian examples), you still buy a Toyota. The umbrella corporate brand is very reassuring to the customer.