"non standard fonts" (that's the fonts which are not in the top section of your font selection list in the field properties) must be fully embedded in order to be usable in fields. You would, however, get a warning message if you specifiy a font which can not be fully embedded (as opposed to the fonts being embeddable as subsets). If you get this message, you will have to either use another font, or organize a version of the font which allows for full embedding.
The other thing is the use or non-use of local fonts. This is a user preference, and you don't have control over it from the document.
In Acrobat (actually Reader) X, as well as in Acrobat/Reader 9, it is in the Preferences --> Page Display tab, Rendering section, where the option is called "Use local fonts". When this is selected, Acrobat/Reader uses the fonts it has on its machine, and not the embedded ones. So, have your user uncheck it (at least for testing purposes), and see what they say.
In older versions, if I remember correctly, it is somewhere in the menus.
Hope this can help.