Any independent priest has to submit to this. And, frankly, this is the #1 problem with "independent priests" and "independent chapels". You have to do your homework. You have to know how well/where the priest was formed and who ordained him.
If he wasn't validly ordained, you're wasting your time of course. It would ALWAYS, IN EVERY CASE be better to stay at home than to attend a simulated "mass".
If he wasn't properly trained, he might have the Character of the Priesthood but not be a true priest. If he wasn't properly trained, he will teach error and eventually give bad advice, become unstable in various ways, have a poor spiritual life (even to the point of being a habitual mortal sinner) or even destroy your group.
A man is made into a priest after 6 years of training. He learns about the spiritual life, his own weaknesses, grows in virtue, and he practices a deeper spiritual life than the average layman. After several years in the seminary, hopefully these virtuous habits will have been cemented. He has superiors who guide him and teach him; they watch him to see if he will be able to fulfill the duties and handle the challenges of being a priest.
Many young men are dismissed during formation for various reasons. Everything from trumped-up/political reasons ("he's too Traditional", "he is against sodomy") to intellectual inadequacy, to grave reasons of moral misconduct -- and everything in between. There are many varied and legitimate reasons why a man might leave -- or be dismissed from -- a seminary before getting ordained a priest.
The Council of Trent declared that priests would be formed in seminaries from now on for a good reason. Look up your history of the 14th and 15th centuries to see what I mean. Protip: Protestantism took root for a reason. The protestants had a fertile soil to grow in: People were scandalized by their poorly trained, ignorant, worldly, womanizing priests.
Anyone can learn to say Mass in a couple of days. Cassocks are for sale online; you can get an adult one for under a hundred dollars. And think of all the ex-seminarians out there from all the seminaries that existed over the past 70 years. That's a lot of men with an above-average knowledge of Latin, liturgy, how priests behave, how to serve (and say) Mass, etc.
So Traditional Catholics need to be on their guard against scammers and frauds, like Ambrose Moran. They do exist. Ambrose is not the only one.
Any group of "ultra conservatives" is going to be more or less desperate for priests. This desperation is the opening for various con men to show up and make a good living.
It isn't just traditional Catholics that have to watch out: any other group that is more traditional than the mainstream needs to be careful: traditional Eastern Rite, traditional Orthodox (like the groups Ambrose Moran hung around in the 80's).
Long story short, a good, valid priest will be happy to show you his ordination certificate, and tell you which bishop ordained him. That bishop should be willing to confirm this fact, if necessary. The Faithful are only doing their job by being prudent. They can't be expected to accept every man with a cassock as a valid priest. God certainly doesn't expect them to.
It's just business. Nothing personal against any of the true Independent priests out there.