As of BPS Pro 8.2 the only place BPS Pro can be updated within the WP Dashboard will be on the WordPress Plugins page with the update now link next to the BPS Pro plugin. We have added code in BPS Pro 8.2 to prevent BPS Pro from displaying or being installable on the WordPress Updates page since this typically leads to this problem – all plugin files (and sometimes additional/other files) being sent to Quarantine.
Did you do the update from BPS Pro 8.1 to 8.2 on the WordPress Updates page or by clicking the update now link on the WordPress Plugins page?