I always thought of the shapefile as an open format, however I cannot be 100% sure for its "openness". I also think that:
a) the (rather justified) term "mostly open" can be translated as "publicly accessible" i.e. without any obvious restrictions to the accessibility of the information itself. Anybody can download a copy without any cost.
b) moreover, a standard is usually something formal and well defined, sometimes abstract, that can be adopted by an organisation (e.g. ISOs are all standards, like the ISO 19115 regarding geospatial metadata)
c) a specification may be (amongst other things) a technical description or an implementation of a standard (e.g. ISO 19115 has an XML/XSD documentation and description)
In this sense, a shapefile is both a type of standard coupled with its specification, as the published document's title implies ("technical description").
If there was a standard related to the shapefile, then it should refer to how the information itself is organised. It should not be tightly coupled with its specification and implementation. A shapefile standard could have other means of implementation.
If someone says that "a shapefile is a widespread format and has become the GIS industry's standard" is a different thing. It does not mean that every single GIS software must support the shapefile format (although that is the trend).
I'd also like to point to the terms included in the PDF of the shapefile's technical description:
Copyright © 1997, 1998 Environmental Systems Research Institute, Inc. All rights reserved.
The information contained in this document is the exclusive property of Environmental Systems Research Institute, Inc. This work is protected under United States copyright law and other international copyright treaties and conventions. No part of this work may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying and recording, or by any information storage or retrieval system, except as expressly permitted in writing by Environmental Systems Research Institute, Inc. All requests should be sent to Attention: Contracts Manager, Environmental Systems Research Institute, Inc., 380 New York Street, Redlands, CA 92373-8100 USA.
The information contained in this document is subject to change without notice.
If the shapefile description was as open as it could be, then the copyright terms could probably be less strict, especially the ones about reproducing the technical description.
Also there should be a place where changes in the specification should be available to anyone.
Finally, the intention of the published document (as stated) is to provide means of data translators.
To conclude, I think that the widespread adoption of the shapefile will soon make it a clearly open standard. It's up to ESRI to express that in written in a future document or a license agreement.
EDIT:::: This text from the Library of Congress is a relevant and useful read (http://www.digitalpreservation.gov/formats/fdd/fdd000280.shtml)