"The rights to this work reverted to the author in 1951" means that back in 1951 the publisher's contract to print the book ended, and the author resumed full rights. (This might have been done by the author, or the publisher, depending on their contract.) It does not mean that the copyright lapsed or that the work entered the public domain. "Ms. Margaret Wilson" was presumably the author or the author's agent, or perhaps the publishers representative back in 1951. She may or may not be alive, and the firm of "Duell, Sloan & Pearce, Inc" may have been the new publisher (unless it was the old one, the question is not clear, and without the title I can't cross check). If DS&P was the new publisher, the rights might now be held by E. P. Dutton, as they seem to have acquired the rights to the bulk of the DS&P catalog.
In any case, the copyright would (if it is in force) now be held by the author's heir, or whoever the author might have sold or given it to. Someone will be the legal owner. That it is not being marketed does not release the copyright or license the work for general use. If there was no other heir, it would have become government property. In the US, it would become the property of the state where the owner was a legal resident.
If this was a work by a US author first published in the US, copyright needed to be renewed after 28 years, which would have been in 1959 (plus or minus one year, I believe). If the work required copyright renewal, and this was not done, then the work is in the public domain, and can be freely used by anyone. Records of copyright renewals, by year, are available for download from Project Gutenberg, or can be searched at the US Copyright Office.
There is no way to be sure how the "scanning institution" determined that "No known copyright restrictions" apply, short of asking that institution. It is possible that they checked for a copyright renewal and did not find one.
If you use content from this work, and the copyright is still in force, the copyright holder or an exclusive licensee could sue for copyright infringement. There is no way to tell if this would in fact happen. It may well be that the legal holder does not even know that s/he owns this copyright. Obviously, in that case, a suit is highly unlikely. But that would be entirely at the risk of anyone who used such content.
Under US law, such use might or might not be considered "fair use". This would depend on several factors, and there is not enough information in the question to even guess. Fair use is an active defense, that an accused infringer may assert in court. It also does not apply in non-US cases.
The odds are probably against any such suit being brought, but the amount at stake if one was brought could be large.