Automated issue solving aims to resolve real-world issues in software repositories. The most popular benchmarks for automated issue solving are SWE-bench and its human-filtered subset SWE-bench Verified. These benchmarks leverage testing to validate generated patches. However, because testing is rarely exhaustive, a patch may pass the tests but nevertheless fail to match the developers' expectations. Unfortunately, it is currently unclear to what extent evaluations performed with SWE-bench suffer from such plausible but incorrect patches. This paper presents an in-depth empirical study of the correctness of plausible patches generated by three state-of-the-art issue-solving tools evaluated on SWE-bench Verified. We extensively test and inspect generated patches, and compare them against human-written ground truth patches. The core of our methodology is a novel technique PatchDiff for differential patch testing, which automatically exposes behavioral discrepancies between two patches. Our findings reveal critical weaknesses in SWE-bench's patch validation mechanism, which causes 7.8% of all patches to count as correct while failing the developer-written test suite. Moreover, our novel automated technique reveals that even more (29.6%) plausible patches induce different behavior than the ground truth patches. These behavioral differences are often due to similar, but divergent implementations (46.8%) and due to generated patches that adapt more behavior than the ground truth patches (27.3%). Our manual inspection shows that 28.6% of behaviorally divergent patches are certainly incorrect. Combined, the different weaknesses lead to an inflation of reported resolution rates by 6.2 absolute percent points. Our findings are a call to arms for more robust and reliable evaluation of issue-solving tools. We envision our automated differential patch testing technique to be useful for this purpose.