Unexpected 'access' (T_STRING) in /ClassLoader.php on line 410

Just updated to WordPress 4.6.1 on a local Trellis setup. Then I was sent to core update as expected, but there I got this error now:

( ! ) Parse error: syntax error, unexpected 'access' (T_STRING) in /srv/www/domain.com/current/vendor/composer/ClassLoader.php on line 410

There is a comment there:

 * Scope isolated include.
 * Prevents access to $this/self from included files.
function includeFile($file)
    include $file;

Still trying to figure this one out. May have to reinstall or update composer.

Well, in the end a composer update on the VirtualBox / Vagrant box did the trick:

vagrant@trainerolo:/srv/www/domain.com/current$ sudo composer selfupdate
Updating to version 1.2.1 (stable channel).
    Downloading: 100%         
Use composer self-update --rollback to return to version 1.2.0

Afterwards the core update was no longer an issue.