Hello Pradyumna
Keep in mind that ICMP echo requests and traceroute are not the same thing. An ICMP echo request (ping) only sends a single probe, and the TTL is always the maximum. Only traceroute will send multiple probes with incrementing TTLs. If the TTL on the traceroute is enough to reach the destination, it will indeed (by default) send three probes to which the destination will respond.
I hope this has been helpful!
Laz