Certain signals may be used to distinguish between illegitimate and legitimate domains. For example, domains can be renewed up to a period of 10 years. Valuable (legitimate) domains are often paid for several years in advance, while doorway (illegitimate) domains rarely are used for more than a year. Therefore, the date when a domain expires in the future can be used as a factor in predicting the legitimacy of a domain and, thus, the documents associated therewith.
In fairness, it is easy to see how this could be interpreted as a signal to register all domains for as long as possible, but for the reasons outlined above there is no likelihood that it will give any SEO advantage (and no evidence either).
the customer service rep was trying to talk me into extending it
To use the famous quote from Mandy Rice-Davies, "well, he would, wouldn't he?".