I don't think you really can tell what type of "dirt" you're picking up on your towel.
Yes, when the lanes and the mmachine surfaces are clena, it is always oil that will be on the ball. If there's dirt on the lanes and/or the machines, the oil will collect the dirt and your towel will show black from the dirt but will also contain the oil, that it takes off the ball. If there's very little oil, the towel can be dirty from plain dirt it picks up or it can be clean if there's little dirt also.
So you must change/wash your towel regularly, because by the time it feels "oily" or greasy, you've already been wiping a ton of oil back onto the ball and the towel is not absorbing oil any longer. Same with a towel that just looks dirty.
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"None are so blind as those who will not see."