Can I trust the driver/software installer downloaded from https://support.apple.com/kb/DL1888?locale=en_GB?
Yes, you can trust it. Only Apple can upload files to support.apple.com. Most of the software there is Apple-authored, although in a few cases I think there may be some third-party software that Apple has decided to supply via their server (but in those cases, I'm pretty sure Apple has checked them thoroughly). The kb page can also be found via https://support.apple.com/downloads/hp.
Also, if you download the the disk image, open it, and then open the installer package inside it, the Installer application will show a padlock in the top right of its window indicating that the package is signed. Click the padlock, and it'll show that it's signed with Apple's &quot;Software Update&quot; certificate. See the &quot;Check Installer packages&quot; section here for a similar screenshot (and lots more discussion about verifying code signatures).