I see that I have DBI 1.623 and DBD::SQLite 1.37 on my Strawberry perl version -- which did reproduce the failure.
Here's the version string for Strawberry perl (I just downloaded the most obvious one from the website today):

C:\>perl -V
Summary of my perl5 (revision 5 version 16 subversion 3) configuration
+:

  Platform:
    osname=MSWin32, osvers=4.0, archname=MSWin32-x86-multi-thread
    uname='Win32 strawberry-perl 5.16.3.1 #1 Tue Mar 12 13:55:20 2013 
+i386'
    config_args='undef'
    hint=recommended, useposix=true, d_sigaction=undef
    useithreads=define, usemultiplicity=define
    useperlio=define, d_sfio=undef, uselargefiles=define, usesocks=und
+ef
    use64bitint=undef, use64bitall=undef, uselongdouble=undef
    usemymalloc=n, bincompat5005=undef
  Compiler:
    cc='gcc', ccflags =' -s -O2 -DWIN32  -DPERL_TEXTMODE_SCRIPTS -DPER
+L_IMPLICIT
_CONTEXT -DPERL_IMPLICIT_SYS -fno-strict-aliasing -mms-bitfields',
    optimize='-s -O2',
    cppflags='-DWIN32'
    ccversion='', gccversion='4.6.3', gccosandvers=''
    intsize=4, longsize=4, ptrsize=4, doublesize=8, byteorder=1234
    d_longlong=undef, longlongsize=8, d_longdbl=define, longdblsize=12
    ivtype='long', ivsize=4, nvtype='double', nvsize=8, Off_t='long lo
+ng', lseek
size=8
    alignbytes=8, prototype=define
  Linker and Libraries:
    ld='g++', ldflags ='-s -L"C:\strawberry\perl\lib\CORE" -L"C:\straw
+berry\c\li
b"'
    libpth=C:\strawberry\c\lib C:\strawberry\c\i686-w64-mingw32\lib
    libs=-lmoldname -lkernel32 -luser32 -lgdi32 -lwinspool -lcomdlg32 
+-ladvapi32
 -lshell32 -lole32 -loleaut32 -lnetapi32 -luuid -lws2_32 -lmpr -lwinmm
+ -lversion
 -lodbc32 -lodbccp32 -lcomctl32
    perllibs=-lmoldname -lkernel32 -luser32 -lgdi32 -lwinspool -lcomdl
+g32 -ladva
pi32 -lshell32 -lole32 -loleaut32 -lnetapi32 -luuid -lws2_32 -lmpr -lw
+inmm -lver
sion -lodbc32 -lodbccp32 -lcomctl32
    libc=, so=dll, useshrplib=true, libperl=libperl516.a
    gnulibc_version=''
  Dynamic Linking:
    dlsrc=dl_win32.xs, dlext=dll, d_dlsymun=undef, ccdlflags=' '
    cccdlflags=' ', lddlflags='-mdll -s -L"C:\strawberry\perl\lib\CORE
+" -L"C:\st
rawberry\c\lib"'


Characteristics of this binary (from libperl):
  Compile-time options: HAS_TIMES HAVE_INTERP_INTERN MULTIPLICITY
                        PERLIO_LAYERS PERL_DONT_CREATE_GVSV
                        PERL_IMPLICIT_CONTEXT PERL_IMPLICIT_SYS
                        PERL_MALLOC_WRAP PERL_PRESERVE_IVUV PL_OP_SLAB
+_ALLOC
                        USE_ITHREADS USE_LARGE_FILES USE_LOCALE
                        USE_LOCALE_COLLATE USE_LOCALE_CTYPE
                        USE_LOCALE_NUMERIC USE_PERLIO USE_PERL_ATOF
  Built under MSWin32
  Compiled at Mar 12 2013 14:01:07
  @INC:
    C:/strawberry/perl/site/lib
    C:/strawberry/perl/vendor/lib
    C:/strawberry/perl/lib
    .
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