Fuses of Arduino Nano are always zero?

Hey, I'm running the following command to get the currently assigned bits of the fuses of my arduino nano (which of course contains inside it the atmega328p)

avrdude -v -p atmega328p -c arduino -P /dev/cu.usbserial-A107B0V0 -b 57600

And get the following output:

avrdude: Version 6.3, compiled on Sep 21 2018 at 19:15:33
         Copyright (c) 2000-2005 Brian Dean, http://www.bdmicro.com/
         Copyright (c) 2007-2014 Joerg Wunsch

         System wide configuration file is "/usr/local/Cellar/avrdude/6.3_1/etc/avrdude.conf"
         User configuration file is "/Users/shaked/.avrduderc"
         User configuration file does not exist or is not a regular file, skipping

         Using Port                    : /dev/cu.usbserial-A107B0V0
         Using Programmer              : arduino
         Overriding Baud Rate          : 57600
         AVR Part                      : ATmega328P
         Chip Erase delay              : 9000 us
         PAGEL                         : PD7
         BS2                           : PC2
         RESET disposition             : dedicated
         RETRY pulse                   : SCK
         serial program mode           : yes
         parallel program mode         : yes
         Timeout                       : 200
         StabDelay                     : 100
         CmdexeDelay                   : 25
         SyncLoops                     : 32
         ByteDelay                     : 0
         PollIndex                     : 3
         PollValue                     : 0x53
         Memory Detail                 :

                                  Block Poll               Page                       Polled
           Memory Type Mode Delay Size  Indx Paged  Size   Size #Pages MinW  MaxW   ReadBack
           ----------- ---- ----- ----- ---- ------ ------ ---- ------ ----- ----- ---------
           eeprom        65    20     4    0 no       1024    4      0  3600  3600 0xff 0xff
           flash         65     6   128    0 yes     32768  128    256  4500  4500 0xff 0xff
           lfuse          0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           hfuse          0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           efuse          0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           lock           0     0     0    0 no          1    0      0  4500  4500 0x00 0x00
           calibration    0     0     0    0 no          1    0      0     0     0 0x00 0x00
           signature      0     0     0    0 no          3    0      0     0     0 0x00 0x00

         Programmer Type : Arduino
         Description     : Arduino
         Hardware Version: 2
         Firmware Version: 1.16
         Vtarget         : 0.0 V
         Varef           : 0.0 V
         Oscillator      : Off
         SCK period      : 0.1 us

avrdude: AVR device initialized and ready to accept instructions

Reading | ################################################## | 100% 0.00s

avrdude: Device signature = 0x1e950f (probably m328p)
avrdude: safemode: hfuse reads as 0
avrdude: safemode: efuse reads as 0

avrdude: safemode: hfuse reads as 0
avrdude: safemode: efuse reads as 0
avrdude: safemode: Fuses OK (E:00, H:00, L:00)

avrdude done.  Thank you.

However - is it true that my fuses are set to zero? all of them are programmed?
It seem like I'm missing something in my understanding on how to read or write these fuses.

My main goal is to enable the CKOUT bit because I would like to measure the clock frequency of with an oscilloscope.

What am I missing? Is there something else I do not understand about the fuses?

Thanks in advance

No, the real value of your fuses is not 0. I think the problem is the bootloader doesn't provide any mechanism for reading the fuses. If you connect an ISP programmer and run the equivalent avrdude command, it will be able to read the correct fuse values. If you don't have a dedicated ISP programmer, you can use an extra Arduino board as an "Arduino as ISP":

Or you might prefer to use this Arduino sketch:
https://raw.githubusercontent.com/nickgammon/arduino_sketches/master/Atmega_Fuse_Calculator/Atmega_Fuse_Calculator.ino
More information about that sketch here:
https://gammon.com.au/forum/?id=11653

A similar situation will occur for writing fuses. You need to connect an ISP programmer to your Nano to do this. You can't do it by just plugging the Nano's USB cable into your computer.

The bootloader doesn't provide functionality for reading the fuses. It can be added. I have such thing for ATmega1284P. However, its min. region for bootloader is 1024B so there is a room for features like this. The 328P has 512B for min. boot region and it is better to save space. The optiboot image for 328P is below 512B.
As I see, you have Nano with old bootloader. It takes 1kB of flash. Old bootloader is little bit bigger. Maybe it would worth for replace it by the optiboot.