I know people who take the same approach to natural language. After all, Spanish and Italian are very very similar, aren't they? The reality with natural languages is that "all languages are the same" thinking enables you to abuse several cultures without actually understanding any of them.
Having seen a fluent southern brazilian portuguese speaker effectively navigate the baja peninsula, I know you're overstating your case. Sure, if you only know one romance language, you'll have vast gaps in your knowledge of another. If you're fluent in one, though, and particularly if you understand its mechanics well on a descriptive/meta level, you can pick up another one much more quickly than if you're learning one for the first time. And in some cases, fluent speakers of one can understand and be understood by speakers of another.
Even if this weren't the case, your objection would have a big problem: programming languages are orders of magnitude more compact and less complex than natural languages. There is, quite simply, a lot less to learn.
And I think that to a large extent the same thing goes for programming languages. For example, if one of your "paradigms" is "object-oriented", does learning Smalltalk really prepare you for making best use of OO in Java or C++? Or vice versa? The inventor of Smalltalk and OO certainly doesn't think so.
SmallTalk would absolutely prepare you to work in Java or C++ in some ways. Maybe not as well as it'd prepare you to work in Ruby or Objective C. Perhaps not as well as C# might prepare you. Definitely better than Pascal would. Paradigms might be a bit more fine grained than "object-oriented", but that doesn't mean that working in one language and (more importantly) understanding the descripting mechanics of it won't dramatically help you with another.
I spent some time a while back trying to explain Scala to a Java programmer. His response was "It's just like Java." Well, Scala *is* just like Java, as long as you ignore the huge and central features that are not like Java. When I started to show him those features, generally in a "replace a page of code with one line" sense, his response was "I don't like it", and that was the end of the conversation. That, in practice, is what "learn 7 languages in 7 weeks" looks like.
No, it's what dislike of the unfamiliar and intellectual incuriosity looks like. The GP posited someone who knew a few paradigms, not someone who didn't like learning new things.
If you want to understand what "learn 7 languages in 7 weeks" looks like, consider part of Daniel Friedman's The Role of the Study of Programming Languagesin the Education of a Programmer ([original postscript] [Google HTML]):
"When I was just starting out in computer science in the Spring of 1964,one of my goals as an undergraduate was to learn at least one new language per semester. ... this was not easy, particularly because languages were not as well designed then. When I went tograduate school, I chose to ratchet up my personal expectations a bit. Now, instead of understanding a language per semester, I wanted to be able to implement a language per semester. Later, I wanted to be able to implement a language per week."