Hi Allison, how to cover your sourdough starter properly can be a confusing subject. The reason we say to "cover loosely" isn't because the starter needs airflow in order to ferment properly (it doesn't), but because a tightly lidded container can cause fermentation gases to build up in the jar, and sometimes you might even seem the lid pop off. However, when you store your starter in the refrigerator the fermentation activity slows down and as long as you have room above the starter level for the gases to accumulate, it's generally fine to put the lid on securely. Even at room temperature, it's important to cover the starter well enough so that the surface of the starter doesn't dry out, so covering with plastic wrap (which will flex) or a loose lid is preferable to covering it with a cloth. 

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