@Claire010, I think you're right to go to the paper and/or DADA2 docs to find more concrete answers, as I haven't spent much time with how exactly DADA2 performs error correction. The Sequence Comparison, Abundance P-value, and Divisive Partitioning Algorithm sections are likely the most useful to you for this.
When we truncate the read at position(Q=2), we do so because we don't trust that read. DADA2 doesn't "save back" the truncated nucleotide, and isn't deciding that we do trust the read. DADA2 is happy to let the untrustworthy data go. It uses its error model to choose likely "true sequences", and replaces likely-erroneous sequences with the likely "true sequence" they most closely resemble.
Incidentally, I think DADA2 author @benjjneb generally recommends using the "base-wise" trim and trunc parameters, rather than trimming by q-score, as this allows DADA2 to rely on max-ee instead of raw q-scores.