I don't really understand the assertion you're saying the other person (people?) is making. Of course lower resources has an impact on the difficulty of a challenge.
In a recent game of mine, the characters were on their seventh combat challenge between long rests and bee-lining it back to town. This is a capable party of experienced players, most of whom are also DMs, some of the characters have higher stats than standard array (rolled them), and all of them have magic items (often weapons and armor). A random encounter came up - a number of veterans and berserkers who proceeded to wreck the party. After a very narrow PC victory, all the players agreed that if they'd had a couple of fireballs (light cleric and a war wizard) left, they could have mowed that encounter down. But they did not and it was only the sup'ed up barbarian that saved their skins.
In my last Planescape game, the PCs were on their fourth combat challenge between long rests when a dozen quicklings came calling. Due to the way the dungeon was laid out, they were able to get in, attack, and get out of sight while the PCs stood there holding their reactions for shield spells (so no OAs). Once they figured out that they should use Con save spells to get the little buggers (thunderwave, shatter), they were down to so few slots that they had to really think about whether they should use shield or cast those spells. Half the party was dying before the final quickling went down. After that, they were completely drained of resources and fled the dungeon to long rest.
These are just two examples of many, many times this has played out. I imagine if someone isn't seeing this in his or her games, there's a high likelihood that the DM is creating and running event-based adventures with set pieces and doesn't often employ time pressures. That would reasonably skew someone's view as to how often a party is depleted of resources.