PHP, 60 bytes

for($a=$argn;$a[$i++]==$a[$i++]&&$r=$i<strlen($a););echo!$r; 

Try it online!

Input string via STDIN, output is truthy (1) if it is double speak, and falsey (0) if it is not double speak. I'm just going to take the +1 byte and make it return an intuitive 1 or 0... even I got confused testing it.