I feel like the more typical reality is an exec looking at the site on some random browser or device, that then has to be in the support matrix, e.g. an enterprise business web app that supports the most recent 2 versions of modern desktop browsers...and the Silk browser for Kindle Fire because that's what's on the CEO's coffee table.
As a person who had to make some custom newsletter compatible with IE8 few years ago, for the 1% who still used it but among of them some were the most important investors, I feel this.
I mean, I get what you're saying, but for a company with critical branding needs, they will absolutely be concerned by this. In many instances they might even notice themselves. Sure, your average software company CEO won't care, but if you're in the food and bev business, or a design firm, or a game developer, the execs are keenly aware that micromanaging their public image is essential. That's why they spend millions of dollars for logo redesigns, or in a more extreme case, spend a huge chunk of change to make their own sliiiightly different version of Helvetica like Target did.
