I grabbed a SparkFun Pocket Programmer to try and confirm the issue. I see this output:
$ avrdude -c usbtiny -p m2560 -v
avrdude: Version 6.3, compiled on Mar 15 2016 at 21:26:45
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/etc/avrdude.conf"
User configuration file is "/Volumes/ElCap/Users/x/.avrduderc"
User configuration file does not exist or is not a regular file, skipping
Using Port : usb
Using Programmer : usbtiny
avrdude: usbdev_open(): Found USBtinyISP, bus:device: 061:001
AVR Part : ATmega2560
Chip Erase delay : 9000 us
PAGEL : PD7
BS2 : PA0
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 10 8 0 no 4096 8 0 9000 9000 0x00 0x00
flash 65 10 256 0 yes 262144 256 1024 4500 4500 0x00 0x00
lfuse 0 0 0 0 no 1 0 0 9000 9000 0x00 0x00
hfuse 0 0 0 0 no 1 0 0 9000 9000 0x00 0x00
efuse 0 0 0 0 no 1 0 0 9000 9000 0x00 0x00
lock 0 0 0 0 no 1 0 0 9000 9000 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 : USBtiny
Description : USBtiny simple USB programmer, http://www.ladyada.net/make/usbtinyisp/
avrdude: programmer operation not supported
avrdude: Using SCK period of 10 usec
avrdude: initialization failed, rc=-1
Double check connections and try again, or use -F to override
this check.
avrdude done. Thank you.
I guess the USBtiny isn't even able to burn a bootloader to this device.
I wonder if it could be bricked by fuses?