Something to note about this strategy is that older versions of IE (10 and older) only support TLS 1.0 by default. Below 8 you're stuck with TLS 1.0 and can't even enable anything higher. So if "https://www.cdc.gov" is using modern web security IE users won't even get to request data from the server, so you can't detect their browser.
To add more info. TLS 1.0 is prohibited from usage by many regulations and it will be immediately flagged by any security audit/tools. The government contract most certainly includes clauses about security and following recommended practices.
In short, anything below IE 11 is de-facto out of the picture.
