I'm a Moscovite, so this answer is bound to be biased.

Safety is a very relative notion, I perceive Moscow safer than quite a few cities I've been to in Western Europe and the US (or at least some of their neighborhoods). Anecdotally, I've once been detained by the US police for several hours out of the blue, so... yes, unexpected things happen everywhere.

>  “I’ll get a rental car, take a taxi or hop on a train if necessary.”

That concern was somewhat reasonable, as you could come across a dishonest taxi driver who would want to exploit you asking for a much greater fare than necessary. I knew a person from the US who paid almost $100 (20 times more than the norm!) for a trip from the airport. Generally, taxis are quite a mess and if you do want to get a taxi, you should first find a reliable taxi company and call them to send a car to your location. Uber and Yandex Taxi might be a good option as well, though I've never used them in Moscow.

The [aeroexpress](https://aeroexpress.ru/en/) trains are a great option if you don't have a car, they're extremely safe, reliable and quick.

The cheapest way to get to the city would be buses and regular suburban trains (look up the directions on the airport's website). In all my life I've never had issues with either of those, but they may be slow (depending on the traffic conditions) and not as comfy.

All in all, all of the public transport (metro, buses, trolleybuses, streetcars and suburban trains) in Moscow is very safe and cheap, though not always as fast and convenient as one could wish for, and may get very jam-packed during rush hours.

> Has the security level for Americans truly degraded to the point that I shouldn’t be taking in the beauty of Moscow on my own, as I try to do in every city I visit, whether traveling on vacation or on business?

I consider it mostly nonsense. That said, you should adhere to the basic tourist wisdom, which is not to let others see you as a confused and helpless foreigner who could easily be taken advantage of. If you're Caucasian and don't wear a striped red, white and blue baseball cap with some stars in the middle, or a t-shirt with the Liberty statue imprinted on it, few people would suspect you to be a tourist from the US.

In conclusion, the succinct advice I would give to anyone visiting Moscow is to not be afraid and visit whatever place you wanted to visit, as long as it's not a military base or something. If you fear the wolves, you'll never get to see the forest, as the old saying goes.

Use the public transport to get to places (and watch some ordinary people in their daily commute!), visit the museums and theatres, try some of the local food, go for a stroll in one of the nearest forests and parks, or leave the hustle and bustle of the city and explore some of the suburbs.

Just:

 - Be aware of your surroundings as always.
 - Don't stand out in a crowd too much.
 - Don't flaunt expensive electronics or fashion accessories in public.
 - Learn the Cyrillic alphabet because not all signs are translated.
 - Don't expect most people (even the police) to speak English or be willing to go the distance to help strangers who don't "even" speak their language
 - Keep the phone numbers of the embassy and your hosts at hand for the unlikely cases of emergency.