First of all that doesn't fit the man page

How does it not fit that quoted statement?

flip at 1? yes
flop at 1? yes      -> Would return false, but must return true once.
flip at 2? yes
flop at 2? yes      -> Would return false, but must return true once.
flip at 2? yes
flop at 2? yes      -> Would return false, but must return true once.
flip at 2? yes
flop at 2? yes      -> Would return false, but must return true once.
flip at 2? yes
flop at 2? yes      -> Would return false, but must return true once.
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Secondly if you look at my third example above, [...] So it can't be a case of flip and flop on the same round, there never seems to be a flip

It flips, but it never flops because $y is always false.

my $x=1;
my $y=0;
for(1,2,3,4,5) 
{
  next  if (printf("flip at %s? %s\n",$_,$x?'yes':'no'),$x)
        .. (printf("flop at %s? %s\n",$_,$y?'yes':'no'),$y);
  print "$_\n";
}
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flip at 1? yes
flop at 1? no      -> Returns true.
flop at 2? no      -> Returns true.
flop at 3? no      -> Returns true.
flop at 4? no      -> Returns true.
flop at 5? no      -> Returns true.
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Update: Truth tables for flip/flop:

..
State	Flip	Flop	New State	Returns
out	yes	yes	out	true
out	yes	no	in	true
out	no	[not executed]	out	false
in	[not executed]	yes	out	false
in	[not executed]	no	in	true

...
State	Flip	Flop	New State	Returns
out	yes	[not executed]	in	true
out	no	[not executed]	out	false
in	[not executed]	yes	out	false
in	[not executed]	no	in	true