Longer version now. The font Janson Text is an old Type 1 Postscript font. If I make a new document in InDesign CC2014, this font is completely available to me. HOWEVER, if I open a legacy file that uses this same font, it shows up with the usual pink highlighting.
I know the font is available to InDesign, because I made a new test document and set type with it.
If I try using the Type > Find Font.. option to replace the 'missing' typefaces, InDesign won't let me, not recognizing the font that I just used in the new test document.
I just tried exporting the defective file as an IDML file, then opening the IDML file. The font is now working properly.
This is a real problem, as the file I'm trying to open is a book that we need to reprint. I now have to go through it page by page to see if any linebreaks have changed.