I wouldn't remove the default nesting of "DOMAIN\Domain Users" from the local "Users" group on member server computers unless you're absolutely sure that you've fully tested the change. For your application, where you're hosting a web based application, you may be just fine. If that application authenticates users and impersonates their domain accounts, though, you may be putting yourself into a nightmare world of troubleshooting. Only you can know this, though.
You're moving away from a default configuration by doing this and my experience is that Microsoft often writes documentation based on the default behavior of their products (and many support resources perform troubleshooting based on an assumption of defaults, as well).
I don't see the harm, personally, in having "DOMAIN\Domain Users" being a member of "Users". I do not see it as a "security breach". Microsoft has taken great care in recent versions of Windows to be sure that the "Users" group is unprivileged. This membership doesn't grant the members things like Remote Desktop capability, ability access "Administrative" file shares, the ability to remotely access the registry, etc.
The onus is on you to test a modification like this and make sure that the environment acts properly in the face of your change. I think your time is better spent making sure you have good password policies, a good IDS/IPS system, well audited firewall rules, good patch application and verification practices, and vulnerability testing of your web applications. This group nesting would not be high on my list of security priorities.