It has never been true, in any way shape or form. It is merely a fallacious argument to inspire fear. At best, one might argue "a vote for a third party is half of a vote for x." Never is it a full vote. How much it's actually worth depends on how you choose to model the voting climate.
Case 1: Not voting
One simple case is to compare voting for a third party vs. not voting. Let's develop a fictitious scenario with two major candidates, Alice and Bob, and a third party candidate, Charlie. We will consider it from the perspective of an Alice supporter, so Alice's argument will be "A vote for Charlie is a vote for Bob." Now let's hypothetically say that the vote results coming in without your vote are:
Now let's say you vote for Charlie, who then loses (as the majority like to claim will always happen). The final vote tally is 1000/1500. But what if you voted? If you voted for Charlie, the results would be
The final vote tally is 1000/1500. In this perspective, voting for Charlie literally had no effect. What if you voted for Bob?
The final vote tally is now 1000/1501. It is quite clear in this point of view, that voting for a third party is not the same as a vote for the other party. The vote for the third party had a different impact than the vote for the other candidate.
Case 2: We own your votes
In some elections, one side portrays the other side as such a vile evil destroyer of all things moral that not only do they make Hilter look like a good guy, but in fact could be so viciously evil when compared to him that the dreaded Hitler mustache comes back in style. (In some cases, both parties may portray the other in this manner, but it turns out that isn't important for this example). In such an election, it is assumed that the votes are naturally going to go towards the good candidate. It is assumed that all votes start as "pledged" for the only candidate worth voting for, and that the evil one sucks them away.
If someone has this point of view, then they may perceive any third party vote as "stealing" from their preferred candidate (Alice in our example). Let's explore a tight race where this might matter:
In this example, I have taken the liberty of "assuming" that you already gave your vote to Alice, who is clearly the only viable candidate from this point of view. Of course, you're a conscious human being, so you can vote the way you want. Let's look at what happens if you vote for a third party instead.
Your vote did change the result of the election. What was once a narrow victory for Alice is now a draw. There may be vote-offs or some other complication to resolve this confusion. You did indeed hurt "the one true candidate" by voting for the third party. But is it the same as a vote for Bob? Let's let you vote for Bob and find out:
Now Bob emerged victorious. This is clearly the single most stressing case possible for this vote, and its being done from the most single-sided viewpoint imaginable. Even in this case, a vote for the third party resulted in a tie. A vote for the other party resulted in the other party winning. Anyone who thinks "A vote for the third party is a vote for the other candidate" clearly does not understand basic arithmetic.
At best we might claim that "A vote for the third party is half of a vote for the other candidate." Consider the first example, with Alice narrowly winning 1251/1250, but now two voters defect to Charlie. Now the situation becomes
Now Bob wins by 1, just like like in the case where your vote went to Bob. However, it took two voters to do this, not one.
Case 3: The counter proposal
Personally, I get tired of this "a vote for the third party is a vote for the enemy" arguments. They are logically false in every way, and people are so fervent about them. Accordingly, I am typically very blunt with them. I ask who their favorite candidate is (we'll assume Alice here) and I say:
So you say a vote for Charlie is a vote for Bob, from your perspective. I thought a third party candidate was a good idea, but you seem to think it's a bad idea. So I'll tell you what. I'll stop voting for my third party: I'll go vote for Bob. By your own wording, a vote for Charlie was a vote for Bob, so you are no worse off than you were before, right? At least not by your perspective.
This typically shuts down their rational parts of their brain and they will start babbling about World War III or the murdering of babies in our inner cities or something like that. In the end, I don't mind. They were going to babble like that anyway, but at least they now know that they can't spout logical falsities like that and get away with it forever.