Knitting For Girls - or - How To Make Your Own History Like The Silence Do.

The Silence construct History in exactly the same way they go about constructing the machines they need. They don't actually build them themselves, they get others to create and build the parts and then they assemble them, reconfiguring the component pieces in a new configuration.

It's never mattered the fact the Doctor didn't actually physically die at Lake Silencio 

Killing the Doctor was never what that whole thing was about - it was about artificially creating the Fixed Point out of the naturally occurring Still Point which existed there.

All they needed was the Fixed Point - it's a component. Add that to the other bits of History they've engineered - and viola! 

You have a stunning twin-set - or - an alternate History, constructed out of the individual bits and pieces that made up the original - taken from different points in time and space and, once brought together, assembled in a new configuration that performs a different function.   
 

All they need is the parts, which they can order for Tuesday

It doesn't matter the order we run into them being either manufactured or put together, when or where or by who. It's just like the way they go about making machines they need. Living organisms are just like other forms of machine to them. See what has actually been happening:

• River talks the Doctor into removing himself from every data base in History - currently, as far as paper goes, he never existed.
• The Silence artificially engineer a Fixed Point where History records the Doctor died.
• River blows up the Tardis allowing the creation of a reality in which the Doctor never existed.
• The Doctor is remembered into existence and memory, just like any other form of data, is editable.

Slap it all together, reconfigure the order and basically you have the situation that - when The Question is asked, when no living creature can fail to answer or answer falsely - the Doctor simply won't be able to answer.