It's a little deeper than that. 
use Devel::Peek;
$! = 0.0;
Dump($!);
stat("non_existing_file");
Dump($!);
die "died at first stat" if -$!;
stat("non_existing_file");
Dump($!);
die "died at second stat" if -$!;

[download]
now yields 
SV = PVMG(0x82c690) at 0x803478
  REFCNT = 1
  FLAGS = (GMG,SMG,pIOK,pNOK)
  IV = 0
  NV = 0
  PV = 0
  MAGIC = 0x804900
    MG_VIRTUAL = &PL_vtbl_sv
    MG_TYPE = PERL_MAGIC_sv(\0)
    MG_OBJ = 0x803460
    MG_LEN = 1
    MG_PTR = 0x8032d0 "!"
SV = PVMG(0x82c690) at 0x803478
  REFCNT = 1
  FLAGS = (GMG,SMG,pIOK,pNOK)
  IV = 0
  NV = 0
  PV = 0
  MAGIC = 0x804900
    MG_VIRTUAL = &PL_vtbl_sv
    MG_TYPE = PERL_MAGIC_sv(\0)
    MG_OBJ = 0x803460
    MG_LEN = 1
    MG_PTR = 0x8032d0 "!"
died at first stat at bug.pl line 6.

[download]
pNOK is now set, but the value hasn't been updated by stat itself. It's only when $! is referenced that the updated value materializes. I certainly wouldn't recommend using -$!, but perlvar says
If used numerically, yields the current value of the C "errno" variable, or in other words, if a system or library call fails, it sets this variable. This means that the value of $! is meaningful only immediately after a failure:
so one can be excused for doing numerical things. It also says
You can assign a number to $! to set errno if, for instance, you want "$!" to return the string for error n, or you want to set the exit value for the die() operator.
and having to assign a non-integer value to avoid surprises doesn't fall in my category of "do what I mean".

In reply to Re^2: Different behaviour of 'stat' function after assignment to $! (errno). by jpl
in thread Different behaviour of 'stat' function after assignment to $! (errno). by muxxum

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