so after some more searching, it appears that they should not.
Rather than delete my question, I'll post the actual content here so if someone googles the question they can actually find the answer (which should already be the case, but it isn't).
The documentation found here does not help understand the functionality, however if you float over the exclamation point next to the query window in TextiQ, far more detail comes up:

Broaden results with '~#'

Consecutive search terms are considered a search phrase, (e.g. formal dress). The order and proximity of terms in a phrase matter. However, order and proximity restrictions can be softened by using the near operator, ~#, where # is a number between 0 and 99.

To use the near operator, a phrase must be enclosed in parentheses or double quotes. For example: (pretty dress )~2 and "pretty dress"~2. The number following ~ determines the number of positions that words in a response can be shifted from those in the search phrase. For example, (pretty dress)~1 will match pretty red dress or pretty red dresses.

Whenever two words in a search phrase are in a different order from a responses, it counts as two position shifts. For example, (pretty dress)~2 will match dress pretty.

If you use ~# with exact operators (see Narrow results with Exact Operators) then each punctuation mark counts as a position and exact rules will be followed. For example, "pretty dress)"~1 will match pretty red dress but not pretty red dresses or pretty, red dress

You cannot use the near operator on complex clauses including clauses with both exact and not-exact phrases. For example, ("pretty" dress)~1 and (dress || skirt)~n are both illegal operations.

I will say that in my experience "pretty dress"~2 vs. (pretty dress)~2 will also exclude "pretty red dresses".
It also seems that sometimes the distance doesn't count common words like and/the, so keep that in mind.
Edit: I will also note that it appears the font Qualtrics has chosen for the forum makes the tilde (~), used in the near operator for textiq, appear as a hyphen if you don't zoom in on the text.

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