Incorrect in some aspects. All caching means is IF a recursive DNS server had done a lookup on your domain recently enough that the TTL hadn't expired, then you use the recursive DNS server's cached copy of the DNS record.
If the recursive DNS server doesn't have a cached copy of the record, it will simply go through the resolution path to get to the authoritative DNS provider and get a fresh copy of the DNS record.
Having a low TTL just means that more queries will hit the authoritative DNS provider since the recursive DNS provider is less likely to have a cached copy of it. It's not bad necessarily to have a low TTL, it just means more queries are generated which results in a little bit longer DNS resolution time compared to using a cached copy. In the case of Dynamic DNS, you are never really going to care/notice any speed hit caused by less caching.