It's not unusual for phones to be jumping between multiple serving sites/sectors depending on traffic loading - the dBm levels you've quoted don't generally suggest any edge-of-cell scenario so therefore a coverage issue doesn't seem to fit.
"Line of sight" in engineering terms is usually taken to mean an issue with a backhaul microwave link, meaning a site is wholly off-air. I presume that the "technical support" person you were talking to was a CS agent rather than an offline network engineer, so this comment leaves me a little puzzled.
If a site is off-air, it's not providing coverage. If it's on-air, then self-evidently it's handling traffic. If they're alluding to a site that's coming & going, then performance stats would be suffering and there may be a balancing act.
