I see the term "intrinsic value" frequently used incorrectly. Mostly, it is used in finance to describe the value of an option when "in the money" (underlying is above/below strike price for call/put). Perhaps they means book value, which the value of the company if all assets and liabilities were sold at market prices. For most pure services companies, it is very low (perhaps negative due to liabilities), as the accounting rules for book value are very strict.
The use I’ve seen in the vernacular is “what are the cash flows worth on their own?” (Discounting back the future ones adjusted for risk) Sometimes people state they know it with confidence, but it’s subjective too (the science on discount rates and predicting growth is a lot weaker than Physics).
It leaves out things like “what might the IP be worth to someone else?” and “What could the company do with better management?”
To your point, it’s frequently less than what the company trades at. Sometimes the opposite is true, and the company trades for less than the cash value of its assets minus liabilities.