Without seeing the terms of service of the host, it is impossible to say. Here are some specific points from your question, and my commentary (based on the text of the law).
- a host takes down content and informs the content creator, it was taken down for copyright reason
- content creator asks to be forwarded the DMCA take-down notification
- after repeated requests and almost 2 weeks later, the host finally provides the DMCA take-down notice
Referring to section (g)(2) from the above link:
(1) No liability for taking down generally.—
Subject to paragraph (2), a service provider shall not be liable to any person for any claim based on the service provider’s good faith disabling of access to, or removal of, material or activity claimed to be infringing or based on facts or circumstances from which infringing activity is apparent, regardless of whether the material or activity is ultimately determined to be infringing.
(2) Paragraph (1) shall not apply with respect to material residing at the direction of a subscriber of the service provider on a system or network controlled or operated by or for the service provider that is removed, or to which access is disabled by the service provider, pursuant to a notice provided under subsection (c)(1)(C), unless the service provider—
(A) takes reasonable steps promptly to notify the subscriber that it has removed or disabled access to the material;
(B) upon receipt of a counter notification described in paragraph (3), promptly provides the person who provided the notification under subsection (c)(1)(C) with a copy of the counter notification, and informs that person that it will replace the removed material or cease disabling access to it in 10 business days; and
(C) replaces the removed material and ceases disabling access to it not less than 10, nor more than 14, business days following receipt of the counter notice, unless its designated agent first receives notice from the person who submitted the notification under subsection (c)(1)(C) that such person has filed an action seeking a court order to restrain the subscriber from engaging in infringing activity relating to the material on the service provider’s system or network.
There is no legal requirement to provide the original DMCA notice to the content creator at all. The bullets I quoted above are entirely lawful behavior on the part of the host.
- the host re-publishes the content, 3 weeks after the counter notice was filled(15 business days), as the complainant failed to sue the content creator
This is suspiciously close to the 14 day maximum allowed for in the law as quoted above. It's possible that the host uses a different definition of "business day," or that they consider the counter-notice received the day after it was sent.
- upon investigation of the PDF file, the content creator notices, that while the notice is dated properly in the letter head, through an XML snippet at the end of the file read with a text editor, the file has in fact been created the day it was received - almost 2 weeks after the take-down.
The notification may have been originally sent on paper, and only scanned after the creator requested it repeatedly. This may also explain why the host was reluctant to provide it.
- content creator has good reason to believe the content was not taken down through a DMCA take-down notice, but through a backroom deal the complainant had with an employee of the host
This makes things worse for the content creator, because that would suggest that the host had "actual knowledge" of an infringing or possibly-infringing item, by some means other than the normal notification process. In that case paragraph (2) does not apply (the removal was not "pursuant to a notice provided under subsection (c)(1)(C)"), and the host has no liability regardless of whether they accept counter notifications at all.
- more importantly though, there's proof(in form of the PDF/XML) the law firm, who filed the DMCA notice, did in fact back-date it, falsifying a legal document
As mentioned above, there is not proof of that. There is circumstantial evidence which tends to suggest it may have happened.
The content creator might, theoretically, have a case to make on the "15 is more than 14" argument, but I would consider it an extreme long shot for several reasons:
- It is very likely that the host's terms of service disclaim liability altogether, or perhaps replace it with a fixed schedule of payments based on specific levels and durations of unavailability. The latter is, in my experience, rare unless the creator is paying a lot of money for the hosting service. If this is indeed the case, then the creator should investigate making a claim for a day's unavailability.
- There is no statutory remedy (and, even if there was one, it might be invalid under Spokeo v. Robins). Any claim would be based on actual damages such as lost advertising revenue. The creator would have to prove those damages with specific evidence, which will be difficult since it's an inherently speculative argument.
- Saying "it was one day late" is going to annoy the judge. Judges don't like this sort of technicality.
- Trials are enormously expensive. Unless the content creator's work brings in a huge amount of revenue, it seems unlikely that they would break even after considering attorney's fees and court costs.