Hi Olivier
Thank you for your solution! I was very happy when it worked on a test image, but I found that it only works well with few ROIs, but starts misbehaving if you have a lot of ROIs (500+) and it seems to be putting 2 or 3 ROIs in each bin. I’ll probably end up splitting the images, but it gets even uglier… 
If all people want is to get measurements of the mean/area, then another workaround is to tick “Display Results” in “Analyze Particles” and then in “Analyze”>“Set Measurements” redirect the measurement to be done in your original image/image of interest.
BUT it looks like myself and Emmanuele need the actual ROIs for further manipulations. Since the “Display Results” works as it should excluding the holes from selection and from measurement (compare results generated from “display results” to results from selecting the ROI in the ROI manager generated by exactly the same action and pressing “Measure”), I conclude that the behaviour of ROI selection is a glitch and it needs to be fixed before damage is done to results of unsuspecting scientists. I am new here and I was wondering, whether it is possible to tag developers to this forum to address this, or we have to go through the normal route of submitting tickets, etc.?