Bridgeman Art Library, Ltd. v. Corel Corp. is still good law and holds, like the preceding case of Hearn v. Meyer, that "slavish copies" of public domain works of art are not copyrightable because the copies lack originality (originality being a requirement for copyright to attach to a work).
There is, therefore, law that supports your position that you may lawfully reproduce "slavish [photographic] copies" of public domain works and then sell those photographs as posters. If you access and reproduce such photographs via Wikipedia it will not object because Wikipedia takes the position that "faithful reproductions of two-dimensional public domain works of art" are themselves in the public domain. [Wikipedia is content, apparently, with "faithful" being a synonym for "slavish."].
But access to the photographs is not the problem nor is making a decent (or even strong) argument that copyright does not attach to the photographs that you want to freely reproduce.
The problem is convincing the person or company who claims ownership of the copyright in the photographs -- someone who has already decided to provide notice to all that its photographs are not to be reproduced w/o permission.
If the copyright of the photograph (as I said before, "such as it is") is registered with the Copyright Office, then there's a statutory presumption that copyright has attached. You would have the burden to prove in court that the photograph lacks the requisite (low) level of creativity and, therefore, cancellation of the copyright registration is warranted because copyright does not attach to the photograph. If the photograph is not registered (either before you allegedly infringe its copyright or within five years of the date it was first published) then the one claiming ownership of the copyright in the photograph has the burden to prove that it's copyrightable. Whoever has the burden of proof is way behind the power curve when negotiating a resolution to a dispute such as this.
As a practical matter, the purported copyright owner will argue that its photograph contains creative elements -- such as lighting the painting in a particular way, including in the photograph some or all of the painting's frame, showing the painting in a particular angle, etc. -- and you would have to argue that the result of such decision-making was not sufficiently creative for copyright to attach to the photograph.
That is the outline of the issues in play. I strongly suggest that you spend some time with a copyright attorney before you decide to copy the photographs that you believe slavishly copy the public domain art you want to sell. At the end of the day, if you freely reproduce the photographs you're taking the fruits of another's labor. As a business practice, that ought to bother you. There could be -- and perhaps should be -- a business solution. Good luck.
For the most part, when you look at art on a website what you're looking at is a photograph, in digital form, of the art (the art being either a painting, drawing, sculpture, photograph, etc.). Someone had to create that photograph and so someone owns the copyright (such as it is) in the photograph. Under copyright law, no one may reproduce the photograph w/o a license from its copyright owner. It does not matter that the photograph shows a separate, copyrightable work that has fallen into the public domain -- the copyright in the photograph is NOT in the public domain.
In short, you cannot lawfully reproduce someone's photograph even if the photograph is of a public domain work. You're butting heads with the "copy of a copy conundrum" which is that it's lawful to copy the original of anything but unlawful to copy a copy of the thing. That is, it's fine to copy onto your medium of choice the image of a model or a landscape or even a public domain work, but it's unlawful to copy someone else's copy of that same thing.
Public domain resources of interest: http://bit.ly/2RJad http://bit.ly/rfz6V
Public domain works are available for use by anyone, and anyone can make their own reproduction by, for example, going to the Uffizi in Florence and taking a high quality photo of Michaelangelo's "David," and turning it into a poster for mass sale.
But that's different than you reproducing the reproductions made by the companies you've found online. If those companies have already made their own reproductions and copyrighted them, or have licensed someone else's reproduction, then they can restrict their use by others.
Another example: Beethover's compositons are in the public domain, so anyone is free to get their own orchestra together and record Beethoven's 5th Symphony. But that doesn't mean that anyone is free to make copies of the LA Philharmonic's recording of that work and sell them -- the composition is in the public domain, but that sound recording is copyright protected.
Disclaimer: Please note that this answer does not constitute legal advice, and should not be relied on, since each state has different laws, each situation is fact specific, and it is impossible to evaluate a legal problem without a comprehensive consultation and review of all the facts and documents at issue. This answer does not create an attorney-client relationship.