That was hilarious! I totally imagined the immigration officer doing that
I just got my experience letter from Infosys where I worked 10 years ago. They wanted exact details, names and email IDs from back then, else they weren’t going to give the experience letter. Given my memory, that was a test in itself!
Most of the companies have their own templates and would not agree to anything other than that. In case of Infy, they allow only 5 bullet points on the experience letter; you cannot exceed that limit. The other experience letter which I got from another company also had their own template but was a little less restrictive.
It might be a good idea to check with your HR on what their format is and ask them if they would be accommodating if you need anything new added to it. Also in my opinion, the experience letter is to establish that you worked for the company in the role mentioned for the time specified. I don’t think they would validate each and every bullet point so a high-level overview should suffice.