It completely depends on what you mean by "access" and where the SSIS packages are stored. Since SSIS packages can be exported as files and then called by the engine from shared locations, then no, you don't have to have administrative privileges on the root machine to access SSIS packages. Just access to the storage location. But, if you mean that you've developed and deployed them all on a single box without using the packages files, then you have to administrator rights to the SSIS server, yes. But that can be set up separately from the SQL Server instance. If it's all in MSDB, you can try assigning database owner privileges there. I think that will work.
SQL Server supports two formats of packages Deployment: **Package Deployment Mode** In this mode, packages can be deployed to file system and then the access is controlled by file system right or to MSDB. When packages are deployed to MSDB, then when you want to grant access, then you have to create a user in MSDB and then access rights are controlled by **`db_ssisadmin`**, **`db_ssisltduser`** and **`db_ssisoperator`** database roles. More details here: [Integration Services Roles (SSIS Service)] **Project Deployment Mode** In this mode the packages are being deployed into SSISDB database and to grant access, you need to create a user in this DB. In this DB, you can assign user to **`ssis_admin`** for administrative access, or you can grant access to individual folders, projects and packages to individual users and/or database roles. You can check for example a post on mssqltips: [Managing SSIS Security with Database Roles] :