Your assumption seems to be correct. I'm using Apache v2.2.16. In 
rpc.php the _SERVER variables contains:

1) with the rewrite rule from the Wiki

   ["QUERY_STRING"]=>
   string(0) ""
   ["REQUEST_URI"]=>
   string(28) "/Microsoft-Server-ActiveSync"
   ["SCRIPT_NAME"]=>
   string(14) "/horde/rpc.php"
   ["PHP_SELF"]=>
   string(14) "/horde/rpc.php"

2) with the Alias rule:

   ["QUERY_STRING"]=>
   string(0) ""
   ["REQUEST_URI"]=>
   string(28) "/Microsoft-Server-ActiveSync"
   ["SCRIPT_NAME"]=>
   string(28) "/Microsoft-Server-ActiveSync"
   ["PHP_SELF"]=>
   string(28) "/Microsoft-Server-ActiveSync"

In both cases Horde::url() does not add the webroot "/horde".

====

As you suggested, I added a local registry.php file with:

$app_webroot = '/horde';        // make sure ActiveSync gets the correct webroot

which correct the problem. The URL is correct now.

Cannot reproduce.

My guess is that either you need to manually set $app_webroot in 
config/registry.local.php or your webserver is either misconfigured or 
not passing the correct value for one of the path-related variables in 
$_SERVER when using an  ALIAS or REWRITE RULE see 
wiki.horde.org/ActiveSync for more information on setting up the 
server rules for ActiveSync.

There is a Preferences for Tasks

Notifications
Choose if you want to be notified of new, edited, and deleted tasks by email:
-> "on all task lists I have read access to"

Don't send me a notification if I've added, changed or deleted the task?
-> not checked

Then I use the "Tasks & Notes" App of Android to add a new Task (or 
alter one).
Then I get a message:

"You requested to be notified when tasks are added to your task lists.

The task "Test Andro" has been added to task list "Steffen Kaiser's 
Task List".
https://<srv>/nag/view.php?tasklist=<uid>&task=0tl7tOj4RqU2D92yNhCgbA1"

nag/lib/Nag.php: sendNotification() is called, but sets

             $view_link = Horde::url('view.php', true)->add(array(
                 'tasklist' => $task->tasklist,
                 'task' => $task->id
             ))->setRaw(true);

with missing webroot

I don't understand this. ActiveSync does not use the web interface at 
all. Where are you seeing this URL?

with

nag                          4.2.4   stable

notifications you get if you add a task via GUI contain the correct URL.

https://srv/horde/nag/view.php?tasklist=uid&task=tsiipIGT9Pv0qlqJBBn7bw1

If you add a task via ActiveSync (Task & Notes for Android), the URL 
is missing the /horde portion:

https://srv/nag/view.php?tasklist=uid&task=0tl7tOj4RqU2D92yNhCgbA1