There is a minimal amount of "default" buffer when you startup a 'screen' session within your 'putty session'. I use screens a lot in my work, so I can tell you that you will not have a combination of 'screen' buffer & 'putty' buffer within your 'screen' session.
Setting the default number of scrollback lines by adding defscrollback 10000
to your ~/.screenrc
file is the correct solution.
By the way, I use "defscrollback 200000" in my ./screenrc
file.