The 'current price' listed on a public stock market for company stock is simply the last price where someone was able to sell their stock to someone else. This is generally a very good representation of current company value, but there are some caveats to using that as 'the value of the company':
(1) For a company where minimal stock is traded (it is 'illiquid'), there are often price lags / jumps up or down, instead of smooth movement. So maybe stock traded 3 days ago for a junior venture at $3 / share, and in 2 days it might jump to $3.50 a share or drop to $2 a share. The more frequently traded a stock is, the greater certainty we have that the recent price is more like market consensus than a one-off need to buy or sell 'at any price available'.
You can see if this is the case by looking at the standing buy/ask orders on the market; if people are lining up to buy at $2 and no one is currently willing to sell for less than $2.75, then it seems the 'market consensus' is just that the 'true value' of a share is somewhere between those two points.
(2) When you buy an increasingly large portion of that company (say, > 1%, 5%, 10%), you are buying more than just the right to future dividends - you are also buying your way to be able to elect at least 1 member of the board of directors entirely on your own, enabling you to have a voice that gets heard in how the company is run. This might enable you to steer the company in a direction you believe to be more profitable or even to interact with your other businesses.
For example, if aluminium became quite rare, Tesla might want to buy a minority interest in some aluminium smelting businesses, in order to be able to gain certainty over its own supply for its production.
buying a significant chunk of shares will quite likely cost more than 'the current market price', for a few reasons:
(a) 1 person recently traded at $3, but perhaps they only have another 10k shares listed at that price, and the next person believes their shares are worth $3.10, so they won't sell for less than that. Large orders can 'gobble up' the order book, and it is unlikely that, say, 30% of a company is currently listed on the order book anywhere close to the last traded price.
(b) If 10% of a company's shares are purchased over a short time frame (especially if it is obvious to be a single buyer), that could create a bit of a 'run on the market', where shareholders may believe rumours about some good news, or even just try to capitalize on someone's immediate need to buy shares, which would further drive up the price.
(c) The value in being able to impact a company's operations has value beyond the currently projected income stream (including for reasons above).
(3) When you buy a controlling interest [ie: 51%, but in cases where there are no other large 'voting blocs', often 30% ownership of a company could allow you to fully vote in the majority of board members, since many small shareholders never vote], you effectively control the company, for all reasonable intents and purposes. Like with the above, this will increase the price you pay to buy the shares, but will also give rise to the need to report your intent and follow regulatory guidelines, which can further drive speculation of the purchase, increasing the price even further.
So, it is not exactly true that someone could take control of, say, TSLA by buying 51% of its 1 billion shares for the current price of $604 each [costing the hypothetical buyer about $302 Billion]. It would likely cost far more than that, because you wouldn't be able to find 500M shares on the open market where the holders are willing to sell for $604, especially after they hear a rumour about someone wanting to buy out the company.
So your executive is being a little glib when he says 'whatever, our market value is still our market value'. The change in current price does reflect a change in market sentiment about the value of your company, and that impacts how much it would cost someone to buy you out, although it would cost more than just the listed share price.