You wrote about the claim 'that Chinese words can mostly be used as any part of speech.' While the claim is untrue, I can see why people fall for it.
The relationship between lexical word class and how they appear as parts of speech is much more opaque than in English. There is nothing close to a one-to-one correspondence between the two, but it would be a mistake to say that there is no correspondence - that would be akin to saying that x and y are unrelated in circles.
In traditional Chinese grammar, the Chinese sentence is made up of six main components:
In English, nouns only belong in the Subject and Object positions, adjectives only belong in adjectival positions, and adverbs only belong in adverbial positions. Verb phrases belong only in predicate positions. Prepositional phrases are more flexible though, and can be objective, adverbial or adjectival.
Yet this is not the case in Chinese. Let's look at where the major lexical categories fit:
Adjectives can go into subject, predicate, object, adverbial and adjectival positions.
Nouns can go to subject and object positions.
Verbs can go to subject, predicate and object positions.
Adverbs can go to adverbial positions.
By the way, clauses and verb phrases can also go to subject and object positions without complementisers.
Here are some examples of constructions that would not be allowed in English:
-Adjectives in adverbial positions (e.g. * *He left sudden* in English but 他突然走了 -he sudden leave-asp. - in Chinese)
-Verbs in subject positions (e.g. * *Swim is fun* in English but 游泳很好玩 - swim very fun - in Chinese)
Note that this does not mean everything works. For example, adjectives can go to predicate positions, but adverbs cannot! You can say
張三的死很突然 (Zhangsan-possessive death very sudden)
Yet you cannot say
*張三的死很忽然 (Zhangsan-possessive death very suddenly)
As a side note, in Classical Chinese, adjectives and nouns can act as transitive verbs, indicating another flexibiltiy in position, but not in Modern Chinese:
Classical: 漁人甚異之 (fisherman very strange it) - the fisherman found it very strange
Vernacular: *漁人很奇異它 (fisherman very strange it)