Not really how it works.
If that was the case, anyone who bought units after Jan 9th wouldn't get the extra units and so would lose half their investment. In reality, everyone who buys units right up to the split date get the 2 for 1. Think about it...otherwise nobody would buy ETE after Jan 9th.
Here is the press release: "The Unit Split will be effected by a distribution of one common unit for each common unit outstanding and held by unitholders of record at the close of business on January 13, 2014. The Unit Split is expected to be completed on January 24, 2014."
I agree with you that if you hold the shares in street name you are relying on you broker to split the shares on Jan 24. However ETE needs to establish ownership dates of unit holders for accounting (K-1) reasons.