According to the "official" LINC site, she is entitled to do the LINC once AIP is received.
I would suggest either going to the office (or sending an email) and show them.
(Hamilton)
http://www.cce.hwdsb.on.ca/Home/ForeignLanguagePrograms/LINCLanguageInstructionforNewcomerstoCanada/tabid/61/Default.aspx
Who can take LINC classes?
LINC is available to adults over the age of 17 who are permanent residents, convention refugees
or those with Approval in Principle status (AIP).
I found the "official" CIC weblink also, which states:
http://www.cic.gc.ca/english/newcomers/before-language-training.asp
Free language training in Canada
The Government of Canada offers free language training across the country to all qualified adult permanent residents—not just people looking for work. The government works closely with provincial governments, school boards, community colleges and immigrant-serving organizations to provide this service.
To qualify for training, adults must:
Have their English or French language skills assessed
Be an adult immigrant (older than the legal school age in your province or territory)
Be either a permanent resident
or a newcomer who has been allowed to remain in Canada to whom Citizenship and Immigration Canada intends to grant permanent resident status and who has not become a Canadian citizen.
As long as she has the official AIP letter they cannot refuse to allow her to take LINC classes.
Edit: Here's a list of all the centres in Hamilton that offer LINC - perhaps going to a different one would be a way of circumventing the idiot you have been dealing with!
http://www.servicesfornewcomers.cic.gc.ca/result.php
"Circle of Friends for Newcomers
151 Queen Street North
, L8R 2V7
Tel.: 905-529-1840
Fax: 905-529-1840
URL:
http://www.cce.hwdsb.on.ca/Home/ForeignLanguagePrograms/LINCLanguageInstructionforNewcomerstoCanada/tabid/61/Default.aspx"
"Hamilton Public Library
55 York Boulevard
, L8N 4E4
Tel.: 905-546-3232
Fax: 905-456-3202
URL:
http://www.myhamilton.ca/myhamilton/LibraryServices/"
"Hamilton-Wentworth Catholic School Board
P.O. Box 2012, 90 Mulberry Street
, L8N 3R9
Tel.: 905-577-0555
Fax: 905-525-1724
Call the office for services and location nearest to you.
URL:
http://www.hwcdsb.edu.on.ca/"
"Hamilton-Wentworth District School Board
100 Main Street West
, L8N 3L1
Tel.: 905-561-2190 x238
Fax: 905-521-2536
Call the office for services and location nearest to you.
URL:
http://www.cce.hwdsb.on.ca/Home/ForeignLanguagePrograms/ESLEnglishasaSecondLanguage/tabid/59/Default.aspx"
"Mohawk College
1400 Main Street West
, L8N 3T2
Tel.: 905-575-1212
Fax: 905-575-2378
Includes services for youth URL:
http://www.mohawkc.on.ca/"
"St. Joseph Immigrant Women's Centre
8 Main Street East, Suite 101
, L8N 1E8
Tel.: 905-529-5209
Fax: 905-521-0541
Call the office for services and location nearest to you. URL:
http://www.stjosephwomen.on.ca/"
"YMCA of Hamilton/Burlington/Brantford
23 Main Street East
, L8N 1E7
Tel.: 905-540-9679
Fax:
Welcome Centre for Newcomers / Programs for Youth"
"Collège Boréal
627 Main Street East, Suite 207
, L8M 1J5
Tel.: 905-544-9824
Fax: (905) 544-6669
(website in French only)<p>Services for francophones.<p> URL:
http://www.borealc.on.ca/index.asp?ref=400&l="
"St. Joseph Immigrant Women's Centre
182 Rebecca Street
, L8R 1C1
Tel.: 905-387-1100
Fax: 905-387-1770
Services for women URL:
http://www.stjosephwomen.on.ca/index.php"
"St. Joseph Immigrant Women's Centre
1119 Fennell Avenue East, Suite 206
, L8T 1S2
Tel.: 905-525-9676
Fax:
Services for women URL:
http://www.stjosephwomen.on.ca/index.php "