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I would say that "fine-tuning" is poorly defined.

This definition from Wikipedia seems sufficiently defined to me:

The fine-tuned universe is the proposition that the conditions that allow life in the Universe can occur only when certain universal dimensionless physical constants lie within a very narrow range of values, so that if any of several fundamental constants were only slightly different, the Universe would be unlikely to be conducive to the establishment and development of matter, astronomical structures, elemental diversity, or life as it is understood.

I heard one physicist say that he can't understand what people mean when they argue that certain parameters in the universe are finely-tuned given that the upper boundary of some of those parameters is infinite.

Which ones are those? Obviously when a scientist is talking about a fine-tuned parameter, he's not talking about one with infinite limits
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