Confusion in using "due to"

Chambers Dictionary has the following explanation:

due to
It is sometimes argued that, because due is an adjective, due to should have a noun or pronoun that it refers back to (an antecedent), as in• • Absence from work due to sickness has certainly not been falling (where 'absence' is the antecedent)• . This argument would disallow sentences like:

?• A special train service was cancelled due to operating difficulties (where due to is effectively a preposition).

This point of view is based on the word's behaviour in its other meanings; in this meaning it has taken on a new grammatical role that is now well established. Due to often refers back to a whole clause even when there is a notional antecedent, as with 'starvation' in the sentence• • Out in the countryside, two million people are at risk of starvation, due to the failure of the harvest.

RECOMMENDATION: it is correct to use due to in both the ways shown

I disagree with calling "due to" an adjective because it isn't describing a noun. A prepositional phrase, yes; an adjective, no.

The sentences in your examples are correct as "due to" is synonymous with "because of."