Welcome to EL&U Ishaan. The sentence is grammatical but is an example of the omission of implied words. The full version of the second clause would be
"...that would be a false assumption if somebody towed it away".
This is not apposition, as you say, because there is no noun which the second clause renames. There is a way to use apposition here though you could say
"Bill might make the assumption that his car is outside, a false one if somebody towed it away."
Here the second part of the sentence renames 'the assumption' which is a noun.
We have replaced the verb 'assumes' with the phrase 'make the assumption' so 'make' is now the verb and 'assumption' is the noun which is the object of that verb.