Getting a positive credit rating is quite simple
I agree completely with this. Commit to debt you can manage, don't overspend on credit cards and you'll be fine.
Income is more important than credit. According to Credit Karma, only 14% of people with an American Express Platinum have a score equal or lower than mine - but Amex gave one to me anyway.
Most people in the US don't have the stomach for the Amex Platinum annual fee and likely don't travel enough for the perks to justify the fee. It's a really unusual card to get first.
Like you mention the Platinum is a charge card, for Amex your income probably had a lot to do with approving you along with the fact that you were applying for a high annual fee card where you pay in full each month. This might not be the case with other lenders or even other Amex products.
There is a an element of randomness in how credit scores are reported and used
There is a lot of randomness. There are three major reporting agencies. All three sell up to the minute credit data, and older less expensive credit data. There are other vendors who sell even different regurgitated credit data from the three bureaus. Depending on how much a particular lender believes in credit scoring they will check some data set which may be older than another and may be different from a different lender and you generally won't know from where data is pulled.
The deviations in your score may just be a time delay, it may also be an algorithm difference and may be a combination of the two. Ultimately your income isn't considered in your credit score and income is likely more important to some lender underwriting departments than credit score and that will be different between different lenders and different types of debt; as you've experienced between the car dealer and Amex.