It's a difficult one to explain. If you were to say "I was nowhere near as late as him!", you are implying that although you were late, you were very close to the time at which the other person arrived.
OR
"Spain is nowhere near as hot as Thailand". This suggests someone has stated that Spain IS a hot as Thailand. In effect, you are saying "It's not even close!".
Using far wouldn't convey the correct meaning or closeness.