You both are right, but there is a caveat: the cells internal resistance.
Connecting cells in parallel is inherently safe if done when they're brought all at the same level; from that moment on they won't charge or discharge across each other because the current draw will always bring them at the same voltage, therefore having zero current from cell to cell.
The problem is however when one or more cells degrade with age, therefore we have more efficient cells in parallel with less efficient ones. That is not a problem safety wise as well, because as before they'll always be at the same potential, but should their degradation change their internal resistance to a point it's a lot higher than their normal one, then we would have the good cells with lower internal resistance sustaining the most current during charge or discharge, and that could be dangerous.
To avoid situations like that one, never implement charges faster than the one that could be sustained by a single cell. Let's say one 2Ah cell can be safely charged at 2C max, that is, 4 Amperes, if we build a pack of 3 of those cells in parallel we would be tempted to charge them at 6C, that is 12 Amperes, which would work in a new pack with all cells that equally balance the current. But if (when) one or two cells degrade their internal chemistry increasing their internal resistance, we'd be left with the remaining good cell(s) drawing the most current, which will largely exceed their individual rating, overheating them and potentially making them explode (that's also when individual cell protection make sense). There's actually a case in which a cell chemistry is so degraded that it can't only store the same amount of current, but also the same voltage, and this could be a problem in parallel packs, but the battery performance drop should have warned us a lot before this happens.
So, all we need is to keep the charge current as low as the current sustainable by a single cell, and we're safe. Slow charging also benefits the overall cells life. Don't worry about connecting unprotected cells in parallel, as they balance themselves: all laptop batteries have balanced series of unbalanced parallels. For example, a 6 cell pack contains is arranged as 2p+2p+2p (2 cells in parallel in series with 2 cells in parallel in series with 2 cells in parallel) while 9 cell packs use 3 cells parallels; series cells are balanced through the BMS, but parallel cells will self balance. What is important is to keep series groups balanced and protect against excessive voltage and charge/discharge current.