「認真」is a common two characters compound word. It means 'serious' (adj.)
Since it is an adjective, we can add the negative function word 「不」(not ) before it, and form an negative phrase 「不認真」(not serious)
However, 「認」on it's own can be the verb 'identify' or ' 'recognize' as in 「認人」(identify a person)，「認路」(recognize the way); while 「真」on it's own can be the adjective 'true' or 'accurate' ; or the adverb 'truly' or 'accurately'
As a simple grammatical rule, an adverb can modify a verb.
Which mean 「認真」 can be treated as a [verb+ adverb] structure instead of a compound that we are familiar with.
In the case of 「認不真」，「不」being a negative function word that modifies the adverb 「真」make it clear that the term we are looking at, is in fact [verb+ 不 + adverb] structure (認+不+真).
If 「不」 is placed before 「認真」, that would make it an [不 + adjective] structure (不+認真).
- 「不認真」means 'not serious'
- 「認不真」means 'cannot identify accurately' or 'not identify accurately'
As I mentioned before, 「認真」is a very common 'word' , to avoid confusion, it is better use 「認不清」 instead of 「認不真」.
I believe if the phrase in question was 「認不真確」instead of the shortened 「認不真」, you would not be so confused.
Since the common word 「認真」is widely used, putting 認 and 真 in a [verb + adverb] structure would certainly cause confusion. It is not recommended.
In this context 須認真 means " Need to identify accurately.
" Need to identify accurately. If not identify accurately, then everything will become (be treated as) fake"
I would suggest phrasing it as 「須認(得)真(確), 若認不真(確), 便都成了假的」 to make it more clear.