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There is some range of tire widths that can fit of specific wheel width. For example, consider this chart, minimum, optimum, maximum, they all are "safe" to fit. Going too wide tires for wheel width will add too much extra flex to sidewalls, handling will suffer, not worth doing unless one is fixated on fitting absolutely widest tires one can for whatever reasons. Going too (hella-)stretched also not advisable, as it will make harder to fit tires w/o hacks, provides only arguable looks for stance crowd, and one will increase risks of tire debeading from wheels, big no-no on track. Then there is common preference of many that track their cars, eg. to tend to fit tires with slight stretch, that is still reasonable, yet extra removes some slop from sidewall flex, sharpening up steering (at slight loss of comfort/compliance). And in this case is i guess tire shop worker generic subjective beliefs of what width goes well and what doesn't.

If you're dropping your car off for them to look at it, I would expect to get a courtesy car. Worth an ask.

Wow that's some difference, nice job.