Our Jenkins servers require "auth-no-challenge" and "no-proxy" flags to be passed to wget when triggering builds.
I installed the Build Root Token Plugin today and attempted to use the buildByToken URI.
It failed. It is not clear why.
The documentation indicates it should "just work".
The only thing different about my environment are the flags which need to be passed to wget.

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Regular URI, is successful:
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$ wget -v --auth-no-challenge --no-proxy https://jenkins.am.blah.com/job/mchon_admin/buildWithParameters?token=SECONDSTREET&FULL_WIPE=false
[1] 22861
mchon@gollum:~/cid-dev/Cid$ 2015-09-04 15:02:30 https://jenkins.am.blah.com/job/mchon_admin/buildWithParameters?token=SECONDSTREET
Resolving jenkins.am.blah.com (jenkins.am.blah.com)... 43.148.4.200
Connecting to jenkins.am.blah.com (jenkins.am.blah.com)|43.148.4.200|:443... connected.
HTTP request sent, awaiting response... 201 Created
Length: 0
Saving to: ‘buildWithParameters?token=SECONDSTREET.3’

[ <=> ] 0 --.-K/s in 0s

2015-09-04 15:02:30 (0.00 B/s) - ‘buildWithParameters?token=SECONDSTREET.3’ saved [0/0]

[1]+ Done wget -v --auth-no-challenge --no-proxy https://jenkins.am.blah.com/job/mchon_admin/buildWithParameters?token=SECONDSTREET

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buildByToken URI, fails:
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{{$ wget --auth-no-challenge --no-proxy https://jenkins.am.blah.com/job/mchon_admin/buildByToken/buildWithParameters?token=SECONDSTREET&FULL_WIPE=false
[1] 22948
mchon@gollum:~/cid-dev/Cid$ 2015-09-04 15:03:33 https://jenkins.am.blah.com/job/mchon_admin/buildByToken/buildWithParameters?token=SECONDSTREET
Resolving jenkins.am.blah.com (jenkins.am.blah.com)... 43.148.4.200
Connecting to jenkins.am.blah.com (jenkins.am.blah.com)|43.148.4.200|:443... connected.
HTTP request sent, awaiting response... 404 Not Found
2015-09-04 15:03:34 ERROR 404: Not Found.

[1]+ Exit 8 wget --auth-no-challenge --no-proxy https://jenkins.am.blah.com/job/mchon_admin/buildByToken/buildWithParameters?token=SECONDSTREET}}