No it doesn’t. Here, let me demonstrate:

I’m accusing you of showing up to my house and kissing my dog (the gay one, not the straight one.)

There. Is that the truth? According to you it must be, because

Accusation = truth

So because it’s true, I demand you restore my dog’s honor by gay marrying him.

And that’s literally how it works in the US. You can make any allegation you want when filing a civil suit and a judge must decide the validity of your claims. Teixiera has given his side of the story when he filed suit; that’s all we can say for certain at this point. He could be 100% right, he could be bending the truth a little bit, or he could be completely lying about the whole thing- we don’t currently have any more information than that.