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The detection of phosphine (PH3) in the atmosphere of Venus has been recently reported based on millimeter-wave radio observations (Greaves et al. 2020), and its re-analyses (Greaves et al. 2021a/b). In this Matters Arising we perform an independent reanalysis, identifying several issues in the interpretation of the spectroscopic data. As a result, we determine sensitive upper-limits for PH3 in Venus' atmosphere (>75 km, above the cloud decks) that are discrepant with the findings in G2020 and G2021a/b. The measurements target the fundamental first rotational transition of PH3 (J=1-0) at 266.944513 GHz, which was observed with the James Clerk Maxwell Telescope (JCMT) in June 2017 and with the Atacama Large Millimeter/submillimeter Array (ALMA) in March 2019. This line's center is near the SO2 (J=309,21-318,24) transition at 266.943329 GHz (only 1.3 km/s away from the PH3 line) which represents a potential source of contamination. The JCMT and ALMA data, as presented in G2020, are at spectral resolutions comparable to the frequency separation of the two lines. Moreover, the spectral features identified are several km/s in width, and therefore do not permit distinct spectroscopic separation of the candidate spectral lines of PH3 and SO2. We present the radiative transfer modelling we have performed and then discuss the ALMA and JCMT analyses in turn.