Ultimately, the police announced they wouldn't proceed with charges, but the issue highlighted a little-known area of the law of theft.
Crimes Act 1958 s 72 neatly explains the law on the point:
72. Basic definition of theft
(1) A person steals if he dishonestly appropriates property belonging to another with the intention of permanently depriving the other of it.
(2) A person who steals is guilty of theft; and "thief" shall be construed accordingly.
When dealing with hard rubbish, the first question will be if the property belongs to another person. There can be no theft of property that is truly abandoned, or is not owned by anyone: R v Thurborn  1 Den 387; (1848) 169 ER 293; Hayes v Fries (1988) 49 SASR 184; 32 A Crim R 394.
However, the evidence in the case must be enough to infer that the owner intended to abandon the property: Moorhouse v Angus & Robertson (No 1)  1 NSWLR 700.
With rubbish, the law works on the assumption that typically what is intended by the owner is merely an intention to transfer title (or ownership) at some time in the future: Munday v ACT (1998) 146 FLR 17; Williams & Roberts v Phillips (1957) 41 Cr App R 5. Both these cases deal with rubbish. The first, was rubbish at a tip that recycled valuable goods. The second was hard rubbish put into bins for collection by a council, but taken by the dustmen. (What a quaint old term!)
In those cases, though the judgments didn't expressly say so, it seems part of the problem was the original owners weren't known and so couldn't say what their intent was and it was left for the court to infer it.
In today's case, I imagine the police were able to find the original owners and ask them what they intended to do with their property.
The other thing to remember is that many, if not all, local council's can regulate hard rubbish collections. Local Government Act 1989 Part 5 provides for local governments to make local laws — sometimes also called by-laws. My local council is typical, providing under local law 710.3:
710. Collection of other refuse
3. A Person must not, without the authority of Council,
a) remove; or
b) interfere with any such refuse, rubbish or recyclable material which is placed out for collection.
(But, though that might create an offence for scavenging, it isn't necessarily determinative of the question of transfer of title. Arguably its purpose is to bestow title, or at least possession, on the council.)
But the critical issue, as is so often the case with theft allegations, is that of dishonest appropriation.
It's here, in s 73(2), that the offence often stands or falls:
73. Further explanation of theft
(2) A person's appropriation of property belonging to another is not to be
regarded as dishonest—
(a) if he appropriates the property in the belief that he has in law the right to deprive the other of it, on behalf of himself or of a third person; or
(b) if he appropriates the property in the belief that he would have the other's consent if the other knew of the appropriation and the circumstances of it; or
(c) (except where the property came to him as trustee or personal representative) if he appropriates the property in the belief that the person to whom the property belongs cannot be discovered by taking reasonable steps.
Often, a person will rely on either paragraph (a) or (b), or both. In the media article above, it seems the police were satisfied that paragraph (a) would apply, and so they elected not to charge the man. It's not necessary for the belief to be correct: so long as it's honestly held, the defence is establish: McCarthy v Hickey, VSC, 7 Aug 1979.
With apologies to Mick Dundee, I have to say that taking a vacuum cleaner ain't a theft: this is a theft:
Some time between midnight and 1 o'clock in the morning on 30th August 2001 a burglar alarm went off at Whetstone golf club in Leicestershire. It was not the sort of burglar alarm which can be heard in the neighbourhood, but one which connected with the police station, and as a result, police officers arrived at the club to find on cursory examination, that it did not appear that the club house itself had been interfered with. However, on looking around, they found in the car park to the golf club, not too distant from the club house, two men dressed in frogman, or diving suits, and in possession of a sack, it can be described in no other way, of very wet golf balls: R v Rostron & anor  EWCA Crim 2206 at .
Although the case must be treated cautiously, because it applies the Ghosh test for dishonesty (used in Commonwealth Code offences, but not Victorian theft charges), it provides a quirky example of when courts will conclude title was not transferred or abandoned, and the accused could not have concluded otherwise.