The button cannot be clicked on my side. For convenience, I prepared a small sample, based on the information that you provided so far and attached it to this thread. Could you please check it and let me know how it differs from your real setup?
Thank you in advance for your patience and cooperation.
Yes, I was able to reproduce this and the button should not work when the textbox is read-only. I have logged this issue on our Feedback Portal. You can track its progress, subscribe to status changes and add your comment to it here. I have also updated your Telerik Points.
Until this is resolved you can use your approach and disable the button.
Should you have any other questions do not hesitate to ask.