That’s both wrong and right.
The odds of the 1000th pull are identical to the odds of the first pull. Check.
But suppose I’m about to push the button to buy a 10x summons. I can ask, what are the odds that, after I push this button, I will have the HoTM? I hope you’ll agree it’s not 1.3%—that’s the chance from just the first summons, but there will be nine more, each of which also has a chance of brining the HoTM.
The correct way to think about this question (if I commit to doing N pulls, what are the odds of getting at least one of a particular hero?) is well established in statistical mathematics.
The way to think about it is like this: what are the odds of not getting my desired outcome? Each roll has a 98.7% probability of not giving me the HoTM. So the probability of not getting the HoTM on two successive summons is 98.7% * 98.7% = 97.42%. So in those two rolls, each of which independently has a 1.3% chance of dropping the HoTM, after doing two rolls there is a 100% - 97.42% = 2.58%. (Notice that this is a bit less than 1.3% + 1.3%; probabilities are not additive).
More generally, if I’m about to do N summons, the likelihood of ending up with the HoTM after those N rolls is 1 - (1-p)^N where p is the probability of getting the HoTM on each roll.
Seriously, this isn’t up for debate. We all get our own opinions, but not our own facts. Math works this way.