This appears to be quite plausible because until 1964 integrated circuits were expensive and unpopular. Leslie Berlin covers the early history of Fairchild in ICs in The Man Behind the Microchip: Robert Noyce and the Invention of Silicon Valley, from which the following quotes are taken.
Fairchild introduced Micrologic in 1961 and attracted a lot of interest. However, despite refusing to license their patents in order to limit competition:
The reaction was gratifying but did not translate into widespread adoption. By the end of 1961, Fairchild had sold fewer than $500,000 of its Micrologic devices, which were priced at about $100 apiece. Texas Instruments, the only other major supplier, was having such problems selling integrated circuits that it cut prices from $435 to $76 in 90 days. The move had little effect.
Customers objected to them because they were expensive, possibly less efficient in certain ways, and because they might limit their own ability to design how they wanted:
If the integrated circuit manufacturers designed and built the circuits themselves, what would the engineers at the customer companies do? Moreover, why would a design engineer with a quarter-century’s experience want to buy circuits designed by 30-year-old employee of a semiconductor manufacturing firm? And furthermore, while silicon was ideal for transistors, there were better materials for making the resistors and capacitors that would be built into the integrated circuit. Making these other components out of silicon might degrade the overall performance of the circuits.
As late as the spring of 1963, most manufacturers believed that integrated circuits would not be commercially viable for some time, telling visitors to their booths at an industry trade show that “these items would remain on the R& D level until a breakthrough occurs in technology and until designs are vastly perfected.
As other answers have mentioned, there were also plenty of production issues in the early '60s:
A brief flurry of customer interest in 1962 proved little more than a frustration because Fairchild could not build circuits in any real quantity. “Inventory on all [Micrologic] short,” Noyce wrote with great irritation in May 1962, “13K [orders] backlog.” He worried that Signetics, the company started by the former Fairchild integrated circuit team, might be first in line to meet customer demand if it ever materialized in any serious way.
So between the production problems and the lack of customer intrest, through 1962 integrated circuits were selling only to the government and military, and not in huge quanitites:
By the end of 1962, Noyce had to admit that the integrated circuit had thus far had “less than a 10 percent effect on our conventional sales.” He called his staff together on a weekend to discuss “how to get more effort on micro ckts [circuits].”
Eventually they would have to start pushing ICs toward commercial customers, but this took a couple of years:
The need to crack the commercial market became more acute after 1962, when Defense Secretary Robert McNamara instituted changes in military procurement and cost-cutting measures that began shrinking the defense market for integrated circuits. (The military would move from buying 100 percent of integrated circuits produced in 1962 to 55 percent of those made in 1965.)
It was in the spring of 1964 that they finally cracked (or created) the commerical market for ICs:
To [Noyce] it was obvious that despite their other purported concerns about the
integrated circuit, customers’ primary objection to the new technology was its cost.... If their technical objections had been met and they still were not buying, the problem had to be the price tag. Accordingly, in the spring of 1964, Noyce made a little-discussed but absolutely critical decision. Fairchild would sell its low-end flip-flop integrated circuits for less than it would cost a customer to buy the individual components and connect them himself, and less than it was costing Fairchild to build the device.
This brazen play for market share leapfrogged Fairchild to the top position in number of circuits sold each year. At the same time, the entire market for integrated circuits took off. In early 1964, industry-wide integrated circuit sales for 1966 were projected to reach $58 million, or 8 million units at an average cost of $7.25 a unit. Within a year of the Fairchild-triggered price drop, estimates had been upped more than 150 percent, to $157 million annually— remarkable growth, given that the average price per unit had dropped.
Less than a year after the dramatic price cuts, the market had so expanded that Fairchild received a single order (for half-a-million circuits) that was equivalent to 20 percent of the entire industry’s output of circuits for the previous year. One year later, in 1966, computer manufacturer Burroughs placed an order with Fairchild for 20 million integrated circuits.
So to summarize, until early 1964 it would be easy for any large customer for ICs to be buying a substantial fraction of total production because the market was just so darn small.