How do I grant the privilege of connecting to SSIS?
I eventually found the solution on MSDN.  To grant users rights to the Integration Services service:


Open Component Services; from a Run dialog, you can enter "dcomcnfg".
On the left-hand tree, navigate to Component Services | Computers | My Computer | DCOM Config.
Find "Microsoft SQL Server Integration Services 12.0".  This is for 2014; I believe earlier versions leave out "Microsoft," so check under "S" if you don't see it under "M".
Open Properties | Security and for each type of permission hit Edit and add an appropriate AD group or user.  Be sure to check the specific permissions required, such as Remote Launch when editing Launch and Activation Permission.  If anyone knows exactly which permissions are necessary for running SSIS, please share.
Launch Services, and restart the SQL Server Integration Services service.


You should now be able to connect to Integration Services from within SQL Studio or dtexec.exe.