I'll take a stab at this but it's not a very well referenced answer, so someone with a better clue is more than welcome to provide a better one.
There are two reasons for this counterargument to be invalid in a vast majority of cases where someone is taxed:
The main reason this is not necessarily a valid counter-argument is that a vast majority of the taxes that libertarians object to are NOT taxes on a held property which someone may have shared-owned before.
A vast majority of taxes being objected to are income taxes. Your income is not something that was previously commonly shared, therefore such a counter-argument doesn't apply.
The only "previously non-owned resource that was shared" that can be claimed as property would be land, or some other natural resources.
Second reason is legal. This one gets really hairy and complicated.
As far as I'm aware, coming into possession of stolen goods in good faith does not make one a criminal, OR liable to return the goods. In other words, if a thief steals your TV and sells it on eBay to me, you can sue the thief. May be you can sue eBay for facilitating the sale. But under current criminal law you're not liable for posession of stolen goods if you didn't know they were stolen (and especially if they were NOT considered stolen under prevalent law of the jurisdiction where they were taken, which is the case here).
One complication is that purely theoretically, you are not entitled to keep possession of stolen goods once the owner makes a motion to recover them.
However, in most jurisdictions, there is a statute of limitations on this. While the intricacies of the law seem... intricate (duh), as best as I can tell, they all start to apply when it is known that the possessor possesses the property; and last several years (2-6 in USA and UK ).
In other words, since the original owner of the property openly held the property and the "everyone" knew of this (most such natural property as land/resources is done in public with the government, so this counts), within several - let's say 3 to 6 years - the statute of limitations on recovery passes, and you can no longer be sued to return the property. TADA. You are now a legal owner, and so are anyone who buys it from you down the road.
In light of that, the only person who "stole" the previously shared resource was the first guy who claimed ownership of that resource, more likely than not many generations ago. As such, even that miniscule amount of private property that your counter-argument MAY have applied to (land/natural resources) is no longer theft once you have purchased/inherited it fair and square after statute of limitations passes.
So, in summary, even if you allow your argument to be valid, the only time it's valid and the taxation is fair under it is if you tax a person who claimed a plot of land or a natural resource (mine, forest, river) that was previously unowned and they didn't pay a prior owner for it.
And to be honest, I'm not entirely sure that there exists a unified libertarian position on whether such "first claim" property ownership should or should not be taxed. I will ask that as a separate question. I asked a follow-up question to clarify: Are there libertarian views on proper procedure to obtain property that was previously unowned?
You can also rephrase the problems with the counter-argument in terms of it relying on a logical fallacy.
It takes the assumption that "some private property is theft", and extends it to "all private property is theft".
I'm going to claim that its that Fallacy of composition, but i'm far from rhetoric expert, so feel free to edit with more correct fallacy.
 - "In most jurisdictions in the United States, the statute of limitations
for actions in replevin ranges from two to six years.23 Similarly, in the
United Kingdom, actions to reclaim personal property expire after six
years24" - "THE THIRD TIME IS NOT ALWAYS A CHARM: THE
TROUBLESOME LEGACY OF A DUTCH ART DEALER - THE LIMITATION AND ACT OF STATE DEFENSES
IN LOOTED ART CASES" by BERT DEMARSIN