That's the key right there. It's NOT believable for the noble on Toril to fall for something he KNOWS to be so against the odds as to be statistically impossible. Imagine if a man who looked completely human knocked on your door tomorrow claiming to be from Ceti Alpha VI. There isn't a reasonable way you could come to believe him.
That's what is happening in the example of a noble from Mystara going to Toril and knocking on the door of the local lord and asking to stay there.
Quite the opposite.
Yup.
Player: "Good day sir, I am Sir PC, and I wish to lodge here tonight, as I am a Noble."
NPC guard: "You're who? Hold on." Closes door.
NPC Castellan: "Good day. You are who?"
Player: "I'm Sir PC, and I'd like to ask lodging here with your Lord."
NPC Castellan: "What is your family name?" "Where are you from?"
Player: "Sir PC Afterthought. I'm not from around here, I'm from Toril, another planet. But I assure you, I am a Noble."
NPC Castellan: "Ah. I see. I am not familiar with that family. My guard will give you a few silvers, you can see yourself to the Inn in town. He will give you directions."
That's about how it would go. If you're a Noble, your mannerisms, dress, carriage, etc. will mark you out as "noble", but if people don't know you, what does it matter.
I have three Nobles in one game I'm running, all children of local Lords and Knights. One is landless, from a disgraced family who lost their lands in the war (also not the eldest), one the eldest of the local Duke. The other the eldest of one of the Duke's Knights, whose family has responsibility over the village where the players began. So, they're all Noble, they know each other, they know the other Noble families and vice versa. But if they went to the neighboring kingdom, without a letter of introduction, their titles might not mean a whole lot depending on the political situation, and whether their Houses have any kind of rep beyond their own kingdoms borders.
They've asked their parents/Houses for horses, and other equipment/accessories, with no issues. The players have organized feasts, inviting other nobles, military officers they encountered, etc. to their house, etc.. and these are low low level characters. Its been completely collaborative.
Its been super helpful that the players are adding to their Houses, and their interrelationships. It would work less well as a "wandering, itinerant Noble" type character.