It may be the reason that +0000 is not a zone id, but a zone offset.

the documentation offers this list:

  Symbol       Meaning                     Presentation      Examples
  ------       -------                     ------------      -------
       V       time-zone ID                zone-id           America/Los_Angeles; Z; -08:30
       z       time-zone name              zone-name         Pacific Standard Time; PST
       O       localized zone-offset       offset-O          GMT+8; GMT+08:00; UTC-08:00;
       X       zone-offset 'Z' for zero    offset-X          Z; -08; -0830; -08:30; -083015; -08:30:15;
       x       zone-offset                 offset-x          +0000; -08; -0830; -08:30; -083015; -08:30:15;
       Z       zone-offset                 offset-Z          +0000; -0800; -08:00;

You may use appendOffset("+HHMM", "0000") (doc) or appendZoneOrOffsetId() (doc) instead of appendZoneId().

so your full formatter may look like the following

DateTimeFormatter formatter = new DateTimeFormatterBuilder()
                .parseCaseInsensitive()
                .append(DateTimeFormatter.ISO_LOCAL_DATE_TIME)
                .optionalStart()
                .appendPattern(".SSS")
                .optionalEnd()
                .optionalStart()
                .appendZoneOrOffsetId()
                .optionalEnd()
                .optionalStart()
                .appendOffset("+HHMM", "0000")
                .optionalEnd()
                .toFormatter();

Further the way of creating a ZonedDateTime may influence if there is an exception or not. Therefore I'd recommend the following as this worked without any exceptions.

LocalDateTime time = LocalDateTime.parse("2013-09-20T07:00:33.123+0000", formatter);
ZonedDateTime zonedTime = time.atZone(ZoneId.systemDefault());

You can build the pattern using DateTimeFormatterBuilder and reuse ISO_LOCAL_DATE and ISO_LOCAL_TIME constants:

    DateTimeFormatter formatter = new DateTimeFormatterBuilder()
            .append(DateTimeFormatter.ISO_LOCAL_DATE)
            .appendLiteral(" ")
            .append(DateTimeFormatter.ISO_LOCAL_TIME)
            .appendPattern("[ Z z]")
            .toFormatter();

    ZonedDateTime dt = ZonedDateTime.parse(date, formatter);

The trick is that DateTimeFormatter.ISO_LOCAL_TIME handles the different number of digit used to represent milliseconds its own. From DateTimeFormatter.ISO_LOCAL_TIME JavaDoc:

This returns an immutable formatter capable of formatting and parsing the ISO-8601 extended local time format. The format consists of:
[..]
One to nine digits for the nano-of-second. As many digits will be output as required.