It’s possible the trans could be going at 170k miles if it has never been serviced regularly but I would not fret over that just yet. I would suggest changing the fluid first.
I think the early Escapes had a transmission dipstick but the 2009s did not. That makes it a bit tougher.
As for the burning smell I have no way of knowing without hands on. It could be a trans fluid leak or engine oil leak. Again. even with this issue don’t fret just yet.
I agree with a second opinion and even a third. Do not tell anyone what the first place told you. And stay away from the transmission chain shops such as AAMCO or Cottmans. I have some personal and not so favorable anecdotes about both.