Yes, you can. Your physician may have a business relationship with a particular diagnostic center and therefore prefer sending you to that particular site. If that imaging center is not Vision Upright MRI Center, you might consider asking for a referral in order to have the ability to stretch out your arms and relax in a quiet atmosphere while being scanned.
Only a doctor can prescribe an MRI, but you do have the right to request a scan in the machine of your choice. During your scan, if you feel like dozing, go ahead. It won’t hurt the scanning process at all and the technologist will give you a gentle wake-up call when your scan is completed.