You can also dual-boot a 64-bit version of Linux and a 32-bit version (I do that) and you'd probably still get those same kind of results.
As for the EULA, whether that's true or not (I wouldn't put it past MS.com mods to say things that are inclined to induce sales, such as saying you need another disc, this time 64-bit) it's not even enforceable in all states or countries. And realistically, there are only legal consequences for large organizations should they be found in violation of the EULA, and it's always for large volumes of violations. It's just not worth the company's time or legal expenses to pursue individual ordinary consumers (and certainly not good for PR). So even if you did break a dubiously quasi-binding EULA, it's not a valid concern for people like you and me.
As for the EULA, whether that's true or not (I wouldn't put it past MS.com mods to say things that are inclined to induce sales, such as saying you need another disc, this time 64-bit) it's not even enforceable in all states or countries. And realistically, there are only legal consequences for large organizations should they be found in violation of the EULA, and it's always for large volumes of violations. It's just not worth the company's time or legal expenses to pursue individual ordinary consumers (and certainly not good for PR). So even if you did break a dubiously quasi-binding EULA, it's not a valid concern for people like you and me.