Incorrect route elevation profile

In a recent trip to the Dolomites I noticed that elevation profile for the active route shown on the altimeter page was incorrect. What could be causing this? When multiple maps are installed, how does the device select which map to obtain elevation data from?

I was using GPSMAP 66i and navigating using routes (not tracks). I had a route for each day. Every single day I noticed that the elevation profile for that day's route was incorrect. In general, the profile coincided with my vertical direction of travel, but it was incorrect with respect to how much I still had to ascend or descend. For example, the profile would show that at a certain point I would have to descend to 5000 feet but in reality I end up descending to say 3700. The same thing happened when ascending. Is as if the altitude data was incorrect in whatever map was being used to fetch elevation data.

But the map elevation doesn't seem to be incorrect. For starters, I had installed two different maps for Italy. Both are based on OSM but from different sources. The contours drawn on the maps showed the correct elevation. I performed routing by enabling/disabling all combinations of the maps (Including the Global DEM) and I would always get the same incorrect profile.

I have yet to try if I can replicate the same thing is the US. Maybe the issue has to do with the maps installed, or not. I just don't know how to determine that.