Incorrect. Looking at 20 years of data: in 16 of them, the first day of Passover and Easter are within 7 days of each other. The exceptions are 2016 (27 days), 2008 (28 days), 2005 (28 days), and 1997 (23 days).
2016 - first day of Passover April 23; Easter March 27
2015 - first day of Passover April 4; Easter April 5
2014 - first day of Passover April 15; Easter April 20
2013 - first day of Passover March 26; Easter March 31
2012 - first day of Passover April 7; Easter April 8
2011 - first day of Passover April 19; Easter April 24
2010 - first day of Passover March 30; Easter April 4
2009 - first day of Passover April 9; Easter April 12
2008 - first day of Passover April 20; Easter March 23
2007 - first day of Passover April 3; Easter April 8
2006 - first day of Passover April 13; Easter April 16
2005 - first day of Passover April 24; Easter March 27
2004 - first day of Passover April 6; Easter April 11
2003 - first day of Passover April 17; Easter April 20
2002 - first day of Passover March 28; Easter March 31
2001 - first day of Passover April 8; Easter April 15
2000 - first day of Passover April 20; Easter April 23
1999 - first day of Passover April 1; Easter April 4
1998 - first day of Passover April 11; Easter April 12
1997 - first day of Passover April 22; Easter March 30