That was certainly true of previous generations of remote control receivers. I fixed a few of those (mostly by retuning). Most of the few garage door and gate opener repairs I've done have been mechanical, not electronic.
Times have changes. For keyless entry receivers, I'm seeing SAW filters, superhets, one-chip receivers, etc. For example: etc...
Whether Genie uses technology that's become standard for automobile door openers and alarms is unknown. Schematics seem difficult to find. Most of the receiver pictures of the boards I've found are obviously TRF (tuned RF) receivers, which will have the detuning problems you mentioned. The more modern opener that Jim bought seems to have a more sophisticated receiver: The black wire on the left is the antenna. Most of the receiver is covered but I can see the leads of an SOT device nearby and no adjustable coils near the antenna lead. That suggests a more modern design, probably using one of the aforementioned integrated receivers, which will not have antenna detuning issues.