They never claimed it would be impossible to shoot down a missile or that any of the technologies involved could not be made to work. Instead, OTA found it was unlikely a program that would be effective against a large scale Soviet first stike could be deployed within the desired timeline.
History has proven them correct.
You can read the actual reports here:
http://fas.org/spp/starwars/ota/
There's a reflexive tendency on HN to dismiss government-directed technology efforts. But a quick look at the advisory panel on the September 1985 OTA ABM report should convince anyone the report authors really did consult with experts in the field:
Guyford Steve, Chairman President, Universities Research Associates
Solomon Buchsbaum Executive Vice President AT&T Bell Labs
Ashton Carter Kennedy School of Government Harvard University
Robert Clem Director of Systems Sciences Sandia National Laboratories
Sidney D. Drell Deputy Director Stanford Linear Accelerator Center
Daniel J. Fink President D. J. Fink Associates, Inc.
Richard Garwin IBM Fellow Thomas J. Watson Research Center
Noel Gayler, Admiral, USN (Ret.) American Committee on East-West Accord
Colin Gray President National Institute for Public Policy
George Jeffs President North American Space Operations, Rockwell International
General David Jones, USAF (Ret.) Former Chairman Joint Chiefs of Staff
Robert S. McNamara Former President of the World Bank
Michael M. May Associate Director-at-Large Lawrence Livermore National Laboratory
H. Alan Pike Program Manager, Space Stations Lockheed Missiles & Space Co.
Frederick Seitz President Emeritus The Rockefeller University
Robert Selden Associate Director for Theoretical and Computational Physics Los Alamos National Laboratory
Marshall D. Shulman Director Harriman Institute for Advanced Study of the Soviet Union
Columbia University Ambassador Gerard C. Smith President Consultants International Group, Inc.
Sayre Stevens Vice President System Planning Corp. Maj. General John Toomay, USAF (Ret.) Consultant
Seymour Zeiberg Vice President Research and Engineering Operations Martin Marietta Aerospace