Nope. Read the Open Source Definition as defined by the Open Source Initiative. To be Open Source (tm), you need to not discriminate against any "fields of endeavor".
The open source initiative failed to obtain the trademark. So "Open Source" as a term is not trademarked, and can mean anything.
IMO, the only useful description of open source is source code licensed under one of the licenses approved by the Open Source Initiative, but there is no trademark protecting that particular use.
http://www.opensource.org/docs/osd#fields-of-endeavor