If it was because the calls (or dereferences; or pre/post increments to the same variable) were "in the same statement", this wouldn't happen:

C:\test>perl -e"{my$x=0; sub X{++$x;\$x}} print qq[${X()}${X()}${X()}\
+n]"
223
[download]

C:\test>perl -e"{my$x=0; sub X{++$x;\$x}} print qq[${X()} ${X()}${X()}
+\n]"
1 23
[download]

But as I understand what's going on, 'this' must happen within a single statement given the clearly defined precedence (in particular, the left-associativity) of the concatenation operator and the particular state-saving behavior of the  X() function in question (note that no pre/post-in/decrement operators were harmed in the following example):

>perl -wMstrict -le
"{ my $x = 0;  sub X () { $x = $x + 1;  return \$x; } }
 ;;
 print ${X()};
 print ${X()} . ${X()};
 ;;
 print ${X;} . ${X;} . ${X;};
 print ${X;} .  'x'  . ${X;} . ${X;};
"
1
33
556
7x89

>perl -wMstrict -MO=Deparse,-p,-q -le
"{ my $x = 0;  sub X () { $x = $x + 1;  return \$x; } }
 ;;
 print ${X()};
 print ${X()} . ${X()};
 ;;
 print ${X;} . ${X;} . ${X;};
 print ${X;} .  'x'  . ${X;} . ${X;};
"
BEGIN { $^W = 1; }
BEGIN { $/ = "\n"; $\ = "\n"; }
use strict 'refs';
{
    (my $x = 0);
    sub X () {
        ($x = ($x + 1));
        return((\$x));
    }
    ;
}
print(${X;});
print((${X;} . ${X;}));
print(((${X;} . ${X;}) . ${X;}));
print((((${X;} . 'x') . ${X;}) . ${X;}));
-e syntax OK
[download]

And yes, I must agree with tye that it's not the sort of code I would wish upon anyone I liked, but it does seem to make sense.