The collar strategy combines one unit of stock with a (long) put option with strike $K_1$ and a (short) call option with strike $K_2$. The payoff of this strategy is exactly $K_1$ if $S_T\leq K_1$, $S_T$ if $K_1<S_T\leq K_2$ and $K_2$ if $S_T>K_2$. The easiest way to see that the statement is false is by comparing the payoff profiles of the collar and that of your statement. Below $K_1$, the payoff is correct $(K_1)$, but for $S_T>K_1$, the payoff diverges.
Start again from the Collar present value
and make use of the Put-Call-Parity, $S+P=C+K$ to arrive at
Please note the emphasis. The payoff profile of a collar is thus achieved by buying / selling calls and entering a bond position with face value $K_1$.