That could very well be a possibility and something that researchers need to address if they wish to investigate this effect a bit further. We can make some educated guesses based on the supplemental table 3. Looking at the staging, grading, tumortype and the hormone receptor status, there don't seem to be any significant differences between the compliant and non-compliant groups. We know that those are the most important factors in assessing how aggressive a breast tumor is, with distinct treatment options and overall survival. So based on this information, I'm inclined to say the cause/effect is not reversed.
Of course, there could be some factors determining aggressiveness and response to chemotherapy that we do not know yet. Unfortunately I'm not in regular patient contact so can't say a whole lot about typical side effect profiles of chemotherapy, but I've heard some anecdotal evidence that for patients treated with immunotherapy, the more severe the side effects, the better the response.