You're right as to a definition of "spaghettification". I was thinking in terms of the dimensionality of space-time as one approaches a black hole, as seen from an outside observer's perspective. ie, a clock would appear to tick more and more slowly, as in the light clock example below.
In Relativity, the effects of gravity and accelerated motion are basically indistinguishable, and so the illustration below can be used to depict either a state of relative motion or a gravitational field.
The graphic below that shows how the space-time frames are increasingly stretched as you get closer to a black hole, or any considerably massive object. The more they're stretched, the more time dilation occurs.
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