I'm guessing you didn't read the paper.
You guess wrong.
But somehow know it must be wrong.
I don't know that either. As far as the data they actually collected, it appears to be correct. But even with my own non-expert reading it was pretty obvious from the start that they were being very selective about what data they actually chose. This is a feature I have learned to notice in papers that are deliberately pushing a specific conclusion; if there is some sort of highly elaborate selection/weighting criteria for their data sets, it's because the researchers know or at least suspect that they won't get the conclusions they expect to get if they collect data from ALL sources unfiltered.
The better papers I've seen actually collect firsthand data from all possible sources and THEN filter the data in various ways to see what conclusions could be drawn from it. Most of the papers I read that use this approach are medical journals and computer science research; they give you the raw data in a big stack of figures and then the researchers walk the readers through the different ways of interpreting those numbers while eventually demonstrating which interpretation is the most likely.
they do not just willy-nilly decide to remove the data sets for employers with multiple establishments, they are excluded because of limitations in the data
Which means they assume a priori that the "limited" data will not be applicable to their conclusions. There's no way they can know that unless they already know what their conclusions are supposed to be.
Specifically:
The data identify business entities as UI account holders. Firms with multiple locations have the option of establishing a separate account for each location, or a common account.
Geographic identification in the data is at the account level. As such, we can uniquely identify business location only for single-site firms and those multi-site firms opting for separate accounts by location.13 We therefore exclude multi-site single-account businesses from the analysis, referring henceforth to the remaining firms as ?single-site? businesses.
Failing to collect multi-site data leaves it ambiguous whether or not the same effect would be consistent with the multi-site data sets. That being true would actually invalidate their conclusion, and their choice to exclude it implies that they KNOW this: a multi-site account having similar results as various single-site accounts despite not actually being in the Seattle area would suggest something other than the wage hike being involved in the effect.
The remaining data covers a large cross-section of minimum wage jobs
It covers a cross section of minimum wage jobs at a specific type of business. To wit, businesses that only have a single location. Common sense alone tells us that a large portion of minimum wage jobs are probably chain businesses like fast food restaurants, convenience stores, gas stations, temp agencies, chain restaurants (Dardan locations, among others) amusement parks, movie theaters, school districts, rental management companies, even housekeeping agencies with more than one office (quite a few of them do).
That data set would literally only include small businesses with extremely limited growth potential and may already be suffering from Seattle's pre-existing marketing conditions in the first place.
There's no particular reason to believe these businesses would behave differently than multi-site businesses
Survey evidence collected in Seattle at the time of the first minimum wage increase, and again one year later, increase suggests that
multi-location firms were in fact more likely to plan and implement staff reductions.
... but since they didn't bother to collect the data on multi-location firms, this is rather difficult to verify, innit?
And again, my reading comprehension may not be all it's cracked up to be, but it APPEARS that this paper is actually using "hours worked" as a proxy for employment and then extrapolating low-wage employment under poorly-defined terms specifically to connect "low wage" to "minimum wage." That would have the effect of attributing a reduction in low-wage hours to the wage hike without being able to rule out that reduction being the result in low wage workers
no longer pulling a low wage.
In any case, it seems quite challenging to argue an economic theory for why the Law of Demand applies in single-site businesses but is magically suspended in multi-site businesses.
As I've said many times, the demand for labor isn't determined by employee wagers, it's determined by customer demand for services. You and many others have this relationship completely ass backwards: wages do not determine demand for labor, demand for labor determines wages. Demand for labor is always -- repeat, ALWAYS -- relatively low for unskilled workers (this should surprise exactly no one) but since automation and high-skilled labor cannot replace those jobs, it never actually reaches zero.
I repeat that this paper and its conclusions are not necessarily incorrect as far as it's worth. It's that the data used to support those conclusions is second hand, VERY incomplete, is very thin on context and depends on a lot of bad assumptions.