That's another moiré!
Yes, the above poster has hit on another source of moirés. By the way, if you want to understand just exactly what a moiré is, get two pieces of screen or sheer fabric and, while looking through them, rotate one against the other. You will see a rather spectacular illustration of just what we're talking about. It's a marvellous phenomena, but not one you want to see on press! If you're at all musical, you can compare this to two instruments playing the same note without tuning to each other - you hear a "beat" between the two, i.e. if one is 440 hz, and the other is 441 Hz, you hear the volume swell and subside at 1 Hz, or once a second. Musicians tune until the beat goes away, then they know they are in tune. It's the same phenomena, only you can see it, your screens are "out-of-tune"!
The above-poster is also correct in noting that your prepress operator should know and be able to explain this to you, and if he/she can't, then... run, screaming, in the opposite direction - they don't know what they're doing. A prepress operator should know how to over-ride your files' settings, or supply you with the correct info specific to your application. If you are giving them EPS files, then yes, your screen angles are probably embedded in the file, but they are easily changed/over-ridden by any decent prepress operation.
Scanning already-screened material can lead to moiré as well, as noted above. The trick is to scan at more than twice the screen frequency, and then "blur" slightly in Photoshop, or use the "median noise" filter to even out any rough spots. I usually scan at four times the required frequency and size and then simply reduce the size in PS, which completely removes any sign of the original screen.
Reproducing highly detailed fabrics or patterns with traditional four-colour screens can also lead to moiré, which is why Sears and others don't use these types of colour seps to print their catalogs. Compare a Sears catalog, or a copy of the Enquirer, to a "normal" magazine with a loupe(magnifier) and you will clearly see the difference.
Keep going, it's called the school of hard knocks, and these hard lessons are the best training there is - you will never forget this lesson - ever.
dmz