Must be up to each immigration officer. I transferred through DOH in October 2016 with a 5-hour connection. Passed through the private Business Class immigration line, told the officer how long my layover was, told him I was going out for dinner, and he stamped me into Qatar with no questions. I then grabbed an Uber and enjoyed a nice walk and dinner in Souq Waqif.
In June 2016 while connecting at BOG, I had a 3-hour layover at 6:00 AM. I told the immigration officer that I needed to exit landside to physically transfer my checked bag as it was between two airlines in different alliances (still Interlined, but wanted to be sure). Stamped into Colombia, got my bag, re-checked it, walked outside for a few minutes, then back through exit immigration.
At NRT I have stamped into Japan with as little as 3 hours layover on multiple occasions just so I could ride the train to Narita town and eat some ramen. Again, no problem. Similar situation (but no ramen), many times, at JNB (South Africa), GRU (Brazil), LHR (UK), FCO (Italy), AMS (Netherlands), AKL (New Zealand), CAN (China), MEX (Mexico), YYZ (Canada), and SCL (Chile).
Maybe what happened to you was an unfortunate mix of bad luck, randomly enforced rules, and variations between different country policies. Regardless, hope you get to Doha sometime...worth it!
(I have a US passport.)