It can definitely get confusing, and I’m personally somewhat confused about what your actual question is because the topic header doesn’t seem to match what you wrote in your post. So let’s take a step back and just look at the basic facts about the Lutron pico remotes and see if that answers your questions. If not, at least we should have a foundation to work from. 
Step 1: the Lutron/SmartThings Integration
Lutron Caseta dimmer switches can work with SmartThings, but only if you also have the Lutron SmartBridge or SmartBridge pro device. (That’s the same device you would need for HomeKit or Alexa or IFTTT integration, by the way.) that allows a Lutron system to communicate with the Internet and your local WiFi, which in turn opens up a bunch of additional integrations.
One smartbridge can support up to 50 Lutron devices.
You can buy the smartbridge by itself, but most people buy it in a “starter kit” which includes one smartbridge, one Lutron Caseta dimmer switch, and one Lutron pico remote.
Note that if you only have a Lutron Caseta master switch, it can only talk to other Lutron switches, which is probably what the person you were talking to you meant by saying it wasn’t “smart home capable.” That isn’t how I would describe it, but there is a real distinction. If you want to get integration with devices of other brands, then you also need the SmartBridge.
In the Amazon picture, the SmartBridge is the square white box sitting in front of the phone.
https://www.amazon.com/Lutron-Wireless-Lighting-Starter-P-BDG-PKG1W/dp/B00MXCRAX8
Step 2: the Pico
The pico is a battery operated device that can be either handheld or mounted on the wall in a frame that will make it the same size as a regular light switch. It comes in several different styles, both a dimmer style and one that just has two plain buttons, and even a 4 button style. You can even get custom engraving if you like.
Now we come to the first part where people get confused. A lot of contractors will say that the pico is “wireless” meaning it is battery operated and is not connected to the other light switches with traveler wires.
Home automation people will say that the pico is “wireless” meaning that it communicates by radio with other devices.
Both are true, but may have different significance in different contexts.
Step 3: how to Pico communicates with other devices
OK, pay attention to this part, because it won’t be confusing if you follow the full explanation, but it will be confusing if you just skip over this part.
A pico has three different possible ways of communicating with other devices.
3A. Direct communication to a specific Caseta master switch
If you don’t have the smartbridge device, you can still pair a pico to a specific Caseta master switch. So when you press a button on the pico, a message gets sent to that master, who will then do what it is asked. So you can use a pico either as a wallmount auxiliary switch for a master in a “virtual three-way” set up or as a handheld controller for the master switch and you don’t need any other devices or any other systems. But the pico can only talk to the specific master that it is paired to.
3B. Communication through the standard SmartBridge device
If you have the standard SmartBridge device, you can set up the official SmartThings/Lutron integration, and now the pico will communicate with the smartbridge. This allows it to control a wider set of Lutron Caseta switches. However, the pico will continue to be invisible to SmartThings. Using this method, smartthings will know when the master switch turns on but it doesn’t know that it turned on because the pico asked it to. And using this method you can’t use the pico button presses for anything else. Just turning on Lutron master switches.
That’s still fine for a lot of people, particularly those who are just looking for a wallmount three-way switch to go with the master.
https://support.smartthings.com/hc/en-us/articles/115000864766-How-to-connect-Lutron-Caséta-devices
3C. Communication via a “man in the middle” server to a smartbridge pro using an unofficial community – created integration
If you have a good technical background, and you get the smartbridge pro instead of the standard smartbridge, you can set up an additional device to act as a server and then you could make the Picos visible to SmartThings. Meaning when you press the button on the pico the smartbridge pro knows it, and that information gets passed along to smartthings. So then you can use a pico for anything that SmartThings can control. A lot of people like to have this functionality, but it is a lot more work to set up, and it is an unofficial integration.
Summary
So to answer the question posed by your topic title, yes, you can use the Picos on their own, but you have to set up another server as a “man in the middle”, you have to use the smartbridge pro model not the regular smartbridge, and you have to use the unofficial integration. All of which is a lot of work, and judging by your first post, isn’t really the question you wanted to ask anyway.
To answer the other questions in your first post, if you use the official integration with SmartThings, you will be able to use the pico’s as the auxiliary wall switches in a “virtual three-way” but smartthings will continue to get all of its information based on the Master switch. And you will require the additional Lutron smartbridge device (the standard model is fine) in order to integrate the Lutron Caseta master switches with SmartThings. And with the official integration, the pico’s remain invisible to smartthings, so you can’t use their button presses for anything except controlling the Caseta master switch.
Did that help clear up any of the confusion?