That certainly is confusing considering your internals. It's possible your IMEI was switched, leading the tool to believe your phone is a D802. Would not be the first time I've seen this. Also, they may have just flashed d802 firmware to your d800 phone. With LG, this can fly in many cases though some limitations may result. Your options are:
1.) try to flash d802 firmware instead, particularly if that works better for your situation. Though it could fail to boot because your phone is not a D802 in reality.
Most likely, worst case scenario is you end up back in fastboot mode though I cannot guarantee that.
2.) hexedit the tot to trick it into believing it's a d802 while actually flashing d800 firmware*
*This is done by opening the D800 tot in a hexeditor and changing the model number from LG-D800 to LG-D802 (or similar wording). Then save, exit and flash. Pro tip on that: most hexeditors have a search feature, so search for "d800". You may see more than once instance of that. Should only need to change the one that lists the full model number, leave the others (if any) alone. Then it will pass the model check.
Sidenote: if we were somehow wrong about it being a d800, this could cause a brick. It'd be ideal to remove the dust covers which cover the mother/daughter boards because I think I remember they are stamped with the actual model number. You seemed to have rather compelling evidence of a D800, but that might help further verify our suspicions. Up to you.
If you want to know what I'd do if it were my phone...I'd go with option 2. Provided that you can live with owning and operating a d800 moving forward. My philosophy is to follow the internals, they don't lie.