10:05 AM PT -- Delta says Tara's got it all wrong. A spokesperson tells TMZ ... first class seats do not allow bags at your feet -- and, as a result, a flight attendant DID suggest Tara put her dog's carrier in overhead ... NEVER the dog itself.

The rep says Tara was told plainly she could keep her dog in her lap or by her feet.

Additionally, Delta says she didn't go quietly and was "very unruly and disruptive" ... according to flight attendants and other passengers.

Tara Reid is drastically changing her story on why she was escorted off a Delta flight -- now saying she was told to stow her dog in an overhead bin, and simply refused.

The actress posted a statement Wednesday clarifying what she says went down Monday when she deplaned a Delta flight from LAX to NYC with her pup. She says the dog is an emotional support animal -- for which she has paperwork -- but Delta's staff still wouldn't let her dog ride on her lap ... only offering overhead or cargo hold storage options.

She says she had pre-arranged to bring the 3-month-old dog on board, but after flight attendants made it clear they were not on board with the plan ... she says she calmly boarded another flight.

You can see and clearly hear from the video ... Tara didn't have a choice -- she was escorted off the plane.

Tara now says we got our reporting wrong, but the fact is ... we spoke directly to her Monday and she told us she was upset about not getting a window seat and feeling cramped in her seat because the person in front of her reclined theirs.

We reached out to Delta to comment on Tara's latest version ... so far, no word back.