Despite deactivating the Office integration, you may still have documents that try to open in the browser.
To work around this, add a bit of script to your site:
jQuery("a[onclick*='SharePoint.OpenDocuments']").each(function (data) { var h = this.href; if (h.indexOf('http') >= 0) { var p = h.indexOf('/', h.indexOf('/') + 1); h = h.substring(p, h.length); p = h.indexOf('/', h.indexOf('/') + 1); h = h.substring(p, h.length); } this.href = '/_layouts/download.aspx?SourceURL=' + h; jQuery(this).removeAttr('onclick'); });