It's cheap to register a domain. Fake WHOIS information may mean that you have a possibility of losing the domain, but if you're doing something sketchy, or just politically unpopular to people who matter, there isn't a paper trail.
Really, a debit card card purchased with cash would probably work just as well, but there are imaginable situations where the risk of losing the domain is less of a problem than being identified as the registrant.
I keep valid contact information in the WHOIS records for my domains, and all I get out of it is e-mail spam from my registrar, e-mail spam from everyone else, snail mail spam from my registrar, snail mail spam from competing registrars (Domain Registry of America, anyone?), "SELL YOUR DOMAIN TO US!" robocall spam, and yearly ICANN WDRP e-mails from my registrar.
You need an anonymized WHOIS service. Namecheap offers free anonymized WHOIS by default on their domains ... its called "WhoisGuard Protection". Its a must have these days.
• who you have to "provide […] truthful, complete, current, accurate and reliable contact details" to,
• who "has the right to disclose your identity and your other Personal Information" and
• who "may resolve any and all third party claims, whether threatened or made, arising out of your registration or use of the Domain"
Now for a lot of people who just don't want their name easily visible, that's fine because it's unlikely these terms will be acted on. But for anyone who actually needs anonymity, to protect their right to free speech (for example), that's not good enough.
If you're looking to actually protect your anonymity when registering a domain, you ought to do so with your own privacy protecting corporation. Delaware corporations (any many offshore corporations) can be legally registered anonymously, which will keep your information off the whois information, without relying on a shaky 3rd party agreement.
