I've heard that before, but I don't really agree. Binary and ASCII encoding, as far as I'm aware, is to do with PostScript. Saving, say, an EPS file with ASCII encoding is the most compatible way of doing it, because it creates a file that uses one byte per charactor of PostScript code. It's like creating PostScript with a text editor. Because PostScript doesn't really need the full range of ASCII charactors, it can take a shortcut, and encode the file differently -- binary encoding.
Binary is more efficient (try saving an EPS file with both encodings and compare the file sizes), but occasionally (actually, very rarely) some software doesn't handle it correctly. In those instances, sometimes saving it using ASCII encoding can help.
There's no technical reason why ASCII & binary encoding should be dependant on one platform or the other. With TIFFs, however, the byte order is directly related to the way the CPU handles data (big & little endian is the technical term). It's not difficult to interpret files destined for another platform, it's just a little more inefficient.