Your point is the same as Scalia's point was when Bush stole the election in 2000
If you're a fact-consumer, you should not say "Bush stole the election".
The best evidence is that the recount that SCOTUS stopped would not have changed the outcome. A different recount that wasn't being done, wouldn't have been done and probably couldn't have been done quickly enough, even if someone had asked for it, which no one did, might have changed the outcome.
For Gore to win (assuming the recount reached the same results as the NORC/media recount), all the following would have had to happen:
1. SCOTUS would have had to remand rather than stay (on Dec 9)
2. FLSC would have had to acted immediately to (a) change the recount to be statewide and (b) direct something very like the maximal standard used by the NORC/media (every other standard found a Bush win). There's no hint that anyone would have asked for either of those things.
3. FLSC would have had to rule that the recount didn't have to be completed by the legislatively-defined Dec 12th "Safe Harbor" date, which most interpreted as the hard deadline. I don't think anyone knows what the probability of that was, but FLSC's previous rulings seemed to imply they wouldn't have.
4. The very careful statewide recount would have to have been completed (including legal arguments and challenges) in at most 8 days. Realistically more like 5, since there absolutely would have been more time-eating litigation.
The most likely outcome if SCOTUS had done nothing is that the recount, if it completed fast enough, would have confirmed Bush's win.
It's also worth noting that another plausible outcome -- Florida just can't make a decision by Dec 18th and sends no electors -- would also have been a Bush win. Without Florida's 25 votes, Gore would have had the most electoral college votes, but wouldn't have had the constitutionally-required 270. In that case, the US House of Representatives would have picked. The result would almost certainly have been a purely party-line vote, 223-211 for Bush.
One final comment: 2000 did not represent some sort of "failure of democracy", and wouldn't even if SCOTUS' intervention actually had changed the outcome. When the electorate is very closely divided, the outcome is determined by random events. Chaos. If a butterfly in Peoria had flapped its wings a couple of months before it could have gone the other way.