Thanks Ovidiu for the tip - I have added

content:encoded<![CDATA[<$MTEntryBody$>]]></content:encoded>

to the Movable Type template that generates my RSS feed, so that the feed contains the full content of entries.

Update: doing this at 1AM I forgot to ask myself about the content namespace (like "self, do you have any idea where this content namespace comes from?"). It is corrected now:

xmlns:content="http://purl.org/rss/1.0/modules/content/"

Thanks again Ovidiu!