No, this is absolutely not the case.

There are plenty of large sites e.g., yellowpages.com and urbandictionary.com (which switched from PHP) which are built using Rails.

Even if you have scaling problems that are around that of, say, Twitter, your application code still isn't your bottleneck; talking to your database is. No amount of framework (or lack thereof, as you propose/promote) will save you from the ramifications of poorly-constructed SQL.