Perhaps I'm late to chime in, but here we go nonetheless...
None of you are "wrong" or having "badwrongfun", but the player's expectations for the game and the GM's are at odds. Default Savage Worlds is probably not the best system for those players...
The thing is - these players will not find the game to be fun if they have their characters "handicapped" for too long - and in the case of Savage Worlds, we're talking literal handicaps, not just the "I'm not in the best shape possible for my character". If the player expects to be playing heroes in a heroic setting, this is very easy to understand - if your character must now behave "unheroicly" for two weeks to have good chances of survival, being stuck with penalties and vulnerabilities might not feel like the best thing in the world.
But of course, in the GM's case, this "realism" is exactly what he likes about the system. If those wounds were unimportant or easily ignored, the game would be less fun and immersive to him.
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Tough conundrum folks. For the GM, it would be a bore to constantly hear the indirect whine of such players. If the wound system is such a problem for those players, it would be fairer of them to simply leave the group or explain to the GM that they don't like such mechanics.
Depending on the situation, changing the game system (or creating house rules) could help both parties. It may be difficult to reconcile a more "heroic/cinematice playstyle" with a more "simulationist/realistic playstyle" though, and in this case, maybe looking for another gaming group would be best.
Since more often than not players at a gaming table are all friends, I suggest that the group talks about the issue. The GM can explain that their comments are making him or her feel unconfortable with the game. The GM should then ask why they are making such comments - and this may be difficult because some people often do not know how to express why they're feeling a certain way and may further shun attempts to understand themselves if it seems they're offending a friend with their actions.
Depending on the gaming group, talking about the issue may have different obstacles to achieve a solution that appeals to everyone.
Assuming the group wants and prefer to stick together, I think that in the "worst case scenario", the GM could rotate position with another player. In that way, they can play the "realistic immersive game" with the current GM and play another more "heroic cinematic game" with another GM. No one gets exactly what they want, but at least there is something for everyone at the table...
My 2 cents, of course. ;P