A EULA can never bind you into a legal contract that has consequences beyond those already provided for by a law or the ability of the copyright holder of the software to deny use of the license.
The EULA is itself purely informal, but informal speech can serve in the provisions of certain laws that look at it to determine the intentions of the two parties. If a law exists that considers whether a user agreed to something in the determination of whether that user must be held to that thing they agreed to, then accepting a EULA is obviously valid under that provision -- but so would an email stating as much.
EULAs are just a list of statements the copyright holder and the user are throwing at each other in bulk format in order to cover those provisions where laws take such statements into account, along with a conditional authorization to use the software. If a EULA does anything else, it will be ignored, as there is generally no law that says "You must do what it says in the EULA". Unless you have one where you live, in which case ouch.
I can say whatever I want in an EULA, but it's going to be worth nothing in court if the user stopped using the license unless I was saying something that directly ties into an existing law. And if they do continue to use the license after doing things I forbid in the EULA, they are committing the specific crime of unauthorized use, since I'm no longer authorizing them.
As much as some EULA writers might get a kick out of writing that you will be tried according to whichever court's law they want, and that you'll be held responsible for XYZ humongous damages if you breach even the tiniest provision even up to two years after you cease using the software... yeah, nope, you'll still get convicted for unauthorized use, not the rest of that crap they listed.
Mind you, I'm repeating what a canadian lawyer explained to me. YMMV and some places may indeed hold the EULA against you.
And blanket statements are always false.