Only a few years after the rise of public Cloud (essentially after a certain online bookshop offered its services to the public) I recall a number of people talking about how open source would no longer matter. The argument, which from 39000 feet made some sense, went something like this: people use open source because closed source equivalents are too expensive, often too difficult to use and generally just a way of accomplishing something "good enough" in a cheaper way. Because cloud offered capabilities, such as web server, messaging, storage etc. to developers on a pay-as-you-go basis, what did it matter if under the covers the implementations were based on closed source or open source? Therefore, people wouldn't approach developing solutions in the cloud by even considering the provenance of the underlying components.
Now of course even at that time you could argue that the argument didn't hold water at all levels. Specifically the operating system back then was predominately Linux based, which last time I checked was most definitely open source. In the intervening years we've seen Microsoft enter the space and whilst Linux is no longer the only operating system available in the clouds it's definitely still the dominant one. But that's not the only thing to change which drives a tank-sized hole in the original position. Today in all public or private clouds you don't have to look hard to find open source making it a reality. Whether it's OpenStack as the infrastructure, databases such as MySQL or MongoDB providing persistence, A-MQ or RabbitMQ for messaging, EAP/WildFly or GlassFish or Tomcat hosting some of the business logic, open source is integral to the success of public, private and hybrid cloud. Obviously there's a chance a developer may not know or even care that open source is responsible for the success of their application or business, but that doesn't negate the fact that cloud is successful today primarily because of open source.
There's also one important aspect that the original argument failed to take into account: users of open source are just one part of the overall value proposition; contributors/developers of open source are just as important. When you look at all of the examples of open source used in cloud I mentioned above, or go further and look at all of the others, you'll see that as well a individuals helping to develop these critical software pieces you've got pretty much all of the significant software vendors of our age as well as many of the most significant software users (verticals such as finance and healthcare, not to mention NASA).
Not exactly related to cloud, but when you get a company such as Microsoft making such an about turn on open source as they've done in the past year or so then it's probably a good bet that open source isn't dropping down the list of priorities for developers or companies. Therefore, to paraphrase and misquote Mark Twain, I think it's safe to say that reports of its death have been greatly exaggerated.