This is a common misconception. You can't use a counter-claim to keep your content up. You can only use one to have your content reinstated after it has been removed.
we had used some images from an mfg's pdf installation manual on a page that was reselling that mfg's own products which we were buying from their offical distributor - the only way to get the product. talk about absurd.
some of the media that they claimed was theirs was in fact our own original graphics/images. it didn't matter, we had to remove everything that was in their overly broad claim.
the DMCA is no joke, but is also a big fucking joke. it's trivial to completely destroy someone's business by simply making fraudulent claims (it's guilty until proven innocent). and it's almost impossible to prove that the claim was made in bad faith rather than simply in error. these claims are usually made by some contracted third party that flags everything that smells off. it's the new patent trolling.
It is very much a joke, and not a joke.
Linode has non-US data centres (eg Singapore). If the node hosting the content was just outside the US, would they need to do a take down? Or is the fact that Linode is a US-based company make this not matter.
Usually, we simply took the content down when it was obvious copyright infringement (Windows ISO images and so on -- yes, people still put stuff like that on their web sites), as that is a TOS violation, and TOS violations is something a host can handle regardless if the legal status of the content. If the customer claimed they owned the copyright on some original content we simply told the people complaining to go through the local courts instead of invoking foreign laws.
Obviously, we have complied in a few cases where one of the new guys handled complaints about businesses' own web sites or subsidiaries' web sites. Laughs were had.
I don't know how a US host acting abroad would handle it though. I suspect they would apply the same rules everywhere.
in addition, how do you show a potential buyer installation diagrams of a technical product without risking your own version being wrong (and not UL-compliant) vs the one in the approved manual?