A tense, worried horse can get strong with a rider, but also agree with
that strong horses may not be particularly tense either.
You can help a tense, worried horse improve, but you may not necessarily prevent a horse from getting strong by training or experience, if they have a certain temperament.
I'll say that I expect horses to learn not to jig and rush at slower gaits, and even if they revert back to some behaviors like that after a lack of exercise from bad weather, injury, etc., I expect them to be responsive again once that problem is overcome. Every horse should be able to learn to relax under normal circumstances at the walk, trot and canter, and feel responsive.
That being said, some horses will always be strong when excited or galloping at times, especially when in groups of horses, open country, or competition. To me this is not a training issue because this can be true for horses that can do very nice canter to halt transitions, for example. It's not that they aren't trained well to cues, but still you may end up with a horse that gets strong at the gallop.
I wouldn't call a horse that ignores cues "strong," but would say the horse does not have enough training, is in the wrong bit or in a circumstances where they are overwhelmed and running off.
To me a strong horse might be one that needs reminders to slow when and where the rider asks, such as half halts or counter-bending as
describes. That horse will push forward strongly and might keep accelerating without these cues, or at top acceleration (full gallop) may need some strong cueing and core strength from the rider to break down into a slower gait. The horse will not ignore the cues, but will feel "strong" or require strong cues for incentive.
A strong horse is an "at times" prospect, while a horse with a training issue will be consistently ignoring or pushing through cues.
I'm perfectly comfortable galloping a strong horse full out, because they will respond to my cues. I will not gallop a horse that is unresponsive to cues, because that is an unsafe prospect.