As soon as I submitted the last message, I remember about the --debug switch --
duh.  I also forgot to mention that /tmp/bogus/bin/hg is my install of crew. 
Sorry for the noise, but here's "push" output with --debug enabled:

$ /tmp/bogus/bin/hg --debug push https://jsquyres@bitbucket.org/jsquyres/proxy-test/
using https://bitbucket.org/jsquyres/proxy-test/
proxying through http://proxy-sjc-2.cisco.com:80
http auth: user jsquyres, password not set
sending between command
pushing to https://jsquyres@bitbucket.org/jsquyres/proxy-test/
sending capabilities command
capabilities: unbundle=HG10GZ,HG10BZ,HG10UN lookup changegroupsubset
sending heads command
searching for changes
common changesets up to ca9e055628d5
1 changesets found
list of changesets:
abdc4e1f661b761cf807a52bcba4e4b1318798de
sending unbundle command
sending 314 bytes
http authorization required
realm: Bitbucket.org HTTP
user: jsquyres
password: <MYPW>
http auth: user jsquyres, password *********
http auth: user jsquyres, password *********
http auth: user jsquyres, password *********
http auth: user jsquyres, password *********
http auth: user jsquyres, password *********
http auth: user jsquyres, password *********
abort: authorization failed
$

Output is pretty much the same with <MYPW> in the URL:

$ /tmp/bogus/bin/hg --debug push
https://jsquyres:<MYPW>@bitbucket.org/jsquyres/proxy-test/
using https://bitbucket.org/jsquyres/proxy-test/
proxying through http://proxy-sjc-2.cisco.com:80
http auth: user jsquyres, password *********
sending between command
pushing to https://jsquyres:***@bitbucket.org/jsquyres/proxy-test/
sending capabilities command
capabilities: unbundle=HG10GZ,HG10BZ,HG10UN lookup changegroupsubset
sending heads command
searching for changes
common changesets up to ca9e055628d5
1 changesets found
list of changesets:
abdc4e1f661b761cf807a52bcba4e4b1318798de
sending unbundle command
sending 314 bytes
http auth: user jsquyres, password *********
http auth: user jsquyres, password *********
http auth: user jsquyres, password *********
http auth: user jsquyres, password *********
http auth: user jsquyres, password *********
http auth: user jsquyres, password *********
abort: authorization failed
$