strict_variables throws exception on checking if variable exists

I'm using a jekyll layout where I want to include content of pages, depending on whether it exists.
Apparently, it is supposed to be done like described in https://github.com/Shopify/liquid/issues/89
In my case it would look as follows:

{% assign title = page.title %}
{% if page.name %}
    {% assign title = page.name %}
{% endif %}
<title> {{ title }} | {{ site.title }} </title>

But since I have strict_variables set to true, which is really useful for development, Liquid throws an exception on building (undefined variable name included).

In my opinion, strict_variables should not throw exceptions for cases where the undefined variable is checked for existance.

The issue does not name specific files or tests. Start by locating the strict_variables handling and the undefined-variable check described here; reproduce the Jekyll-style conditional, then verify that checking for an absent variable does not raise while genuine undefined-variable uses remain strict.