So I decided to try to open the file in Acrobat to investigate what might be wrong. But instead Acrobat opening the file, I got the following message: "There was an error opening this document. The file is damaged and could not be repaired."
I decided to try an alternative to Acrobat. For certain tasks, I like to use Apple's Preview software. So just out of curiosity, I wanted to see if Preview would save the day for me as it has on several other occasions. So, I opened the same file in Preview and it opened without any problem whatsoever. I saved it with a different name and then imported the file into InDesign.
Out of curiosity, I checked out the file in Acrobat. All the fonts were embedded properly, and everything checked out properly from a prepress-standpoint.
I'm not sure what the problem was, but it sure is good to know that I have a workaround to rescue problematic PDF files when they don't want to open.