When I used my InterRail pass (I have to admit it was a few years ago) my passport was checked about every other time.
Now is my passport on of a participating country so that one check was enough.
At that time you had to have been a resident in one of the participating or other allowed European countries for 6 months or longer. That requirement seems to be changed into being a 'resident'. So you would not need to proof having been in Europe, just the intent and possibility of being a resident.
So if you have a passport (or ID card) which allows you to be a resident in one of the InterRail countries, you will likely be able to use InterRail instead of Eurail.
But if your passport would require visa for an extended stay in Europe, it is likely you will not be able to pull it off, even if you can buy the pass.
One of the reasons InterRail passes are cheaper for adults is that they do not require buying first class passes, they also offer standard class, (or whatever it is called locally) and that class of travel will get you there as fast.
Not the topic of the question but something to consider, often separate tickets are as cheap or cheaper than a pass. Certainly if you do not want to do a lot of long distance train travel. Specially useful if you book early.
Early bought restricted use tickets can be as cheap as the surcharge you need to pay for a train using the pass. But it does require planning and willingness to fix the travel beforehand.
An other option is making a lot of short hops, which are often cheaper than the rail pass is per day.
Also see the site of the Man in Seat 61, rail passes pages.