It's funny how things seem to bob to the surface every so often, a bit like revivals of Musicals or the fact you know it's christmas becuase ET is on the TV again.
Blake Morrision from the Ask the Performance Team has blogged about issues with working sets and SQL Server, http://blogs.technet.com/b/askperf/archive/2012/01/25/real-life-sql-working-set-trimming-issue.aspx
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I blogged about this back in March 2009 http://sqlblogcasts.com/blogs/grumpyolddba/archive/2009/03/18/x64-memory-problems.aspx and at the time deployed the dynamic cache service to deal with this exact problem.
Personally given the circumstances I'd never allow a third party backup tool onto a production SQL Server, my preference is to ship or replicate backups to another location where the streaming to tape can occur without any impact on the Production Server.
I also don't slavishly apply lock pages in memory, my view is that if you have to set this to stop memory paging it would be a far better option to find the root cause and fix that rather than sweeping it under the table - no doubt many will not agree with me on this!