Maybe it just comes down to how you think about Indy.
Seeing as much of the series' entertainment value to me stems from Indy's near-misses and recurring inability to do exactly as he intended, I'm not sure I personally see the believability issue.
Sure, a 75 year old wouldn't make a good Jason Bourne, or James Bond, or Batman, or Lara Croft type super action hero who flawlessly executes every stunt. But Indy? That's a little easier for me to buy.
The other thing is, it's just for this this ONE movie. Unless they surprise us with some back to back situation, this is the only time we're ever going to get an Indy this old. After this, those of you who really, really want a young buck Indy are going to get just that for an eternity of reboots.
You can't let Indy be old just this one time? You can't let those who want this enjoy it without your incessant complaining, just because you can't get your way for one more movie?