Ultimately, I ended up avoiding the query function entirely by using the filter function instead:
=COUNT(FILTER('Form Responses'!$A$1:$F$100; DATEVALUE('Form Responses'!$A1:$A100)=DATEVALUE('2013-11-19'); 'Form Responses'!$B1:$B100='Ajedi32'))
Expanded for readability:
=COUNT(
FILTER(
'Form Responses'!$A$1:$F$100;
DATEVALUE('Form Responses'!$A1:$A100)=DATEVALUE('2013-11-19');
'Form Responses'!$B1:$B100='Ajedi32'
)
)
(If anyone still wants to have a go at answering my original question, feel free.)