The problem is not solved but now I know exactly why. This "Table1" thing wasn't a named range but a table, which I can access through the "Tables" collection of the worksheet.
Now, the problem is that both the Tables' collection and Table objects in EPPlus are readonly so I can't define the table's dimension from my code, and neither can I remove it or add a new one to fit my needs. EPPlus's author has already mentionned that it might someday be implemented (here and here) bus as the messages are almost 3 years old, I guess there is little hope to see that happen...
Anyway, I hope this will help anyone encountering the same issue.
[EDIT] I finally came up with a way to bypass the problem : the ExcelTable object has a writable property called "TableXml" which contains the xml definition of the table with - of course - its range. Here's its content in my case :
<?xml version="1.0" encoding="UTF-8" standalone="true"?>
<table dataCellStyle="Normal 2" headerRowCellStyle="Normal 2" headerRowDxfId="70" totalsRowShown="0" insertRow="1" ref="A1:U2" displayName="Table1" name="Table1" id="1" xmlns="http://schemas.openxmlformats.org/spreadsheetml/2006/main">
<autoFilter ref="A1:U2"/>
<tableColumns count="21">
<tableColumn dataCellStyle="Normal 2" name="Activity" id="1"/>
<tableColumn dataCellStyle="Normal 2" name="Category" id="21"/>
[...]
<tableColumn dataCellStyle="Normal 2" name="Closed Year" id="20" dataDxfId="62"/>
</tableColumns>
<tableStyleInfo name="TableStyleMedium9" showColumnStripes="0" showRowStripes="1" showLastColumn="0" showFirstColumn="0"/>
</table>
What interests us here are the "ref" attributes in the "table" and "autoFilter" nodes, as changing their values allows to redefine the range of our table.
I proceeded this way :
XmlDocument tabXml = sheet.Tables(0).TableXml;
XmlNode tableNode = tabXml.ChildNodes[1];
tableNode.Attributes["ref"].Value = string.Format("A1:U{0}", dt.Rows.Count + 1);
XmlNode autoFilterNode = tableNode.ChildNodes[0];
autoFilterNode.Attributes["ref"].Value = string.Format("A1:U{0}", dt.Rows.Count + 1);
And now my Excel file is properly generated with "Table1" fitting the actual range of my data !