That statement is generally true but with emphasis on 'no recovery' and 'every ride'. If you're indeed riding Tempo and Threshold every time you get on the bike and not taking any rest days or any easier days then some recovery in your workout week is likely in order. But the basic premise that there's a 'no man's land' that should be avoided while training or that most or even many riders do too much Tempo and Threshold while trying to improve base aerobic fitness (i.e. during build as opposed to race phases of their training) is a very old concept that's been debunked many times over the years but the belief dies hard with some including apparently this author.
If those hills that are giving you fits are short 'sprinter's hills' in the thirty second to say two minute range and your riding partners are getting up and absolutely hammering them the idea of needing to have some event day freshness to deal with the big pace changes might make some sense and in many road races that's exactly what will happen on courses like that and racers definitely wouldn't want to show up for races like that with heavy fatigued legs from too much recent training and too little recovery. But if you're talking about longer climbs in the saddle where your riding partners pull away from you steadily then it comes down to sustainable watts per kilogram of body plus bike weight. So increase the sustainable watts (and a lot of Tempo/SST/Threshold riding is a very good way to do that for riders that lack the time to train four or five hours day in and day out) or drop weight.
But yes, mental attitude and things like gearing as you approach and transition onto the hill can make a big difference as well. If you're dropping down into your triple's granny gear or very low gearing at the first sight of the hill you're likely giving away a ton of momentum and letting gaps open up before the climbing even starts. Gearing down enough not to lug down and end up over geared is smart but spinning your brains out as you slide backwards won't help you sustain power up the hill either but it's pretty common for folks worried about climbs to over compensate and try to spin crazy low gearing up modest climbs....they just go slow as a result. So play with gearing, don't wait till you stall out but try riding some hills in training in a bit bigger gears if you typically spin very low gears up climbs. It's o.k. to grind a bit and stand up occasionally to regain momentum on steeper bits. Similarly if you always grind up hills, try downshifting progressively on the climb to avoid stalling out in too big a gear. IOW, experiment with gearing and try to find a gear that offers some solid resistance but that you can still turn over and don't downshift for every slight increase in terrain if a handful of out of the saddle pedal strokes can get you over those bits.
Work on your out of the saddle technique to find a gentle rocking rhythm that allows you to drop your body weight on the pedals as you use your arms to rock the bike from side to side. There are different ways to do this for different situations like attacking, dealing with a steep bit or just standing to rest and change up your muscle loading a bit on longer climbs. Play with it and for if it's rest or muscle changeup you're after try shifting up a cog or two before you stand so you don't lose speed as your cadence naturally drops while standing. Little things like that can make a big difference as can things like sliding aft on your saddle while climbing to bring different muscle groups into play which again works best if you're not spinning crazy easy gears on modest climbs.
Don't try to attack the bottom of longer climbs but do try to at least match the pace of your riding companions and try to settle into a pace that keeps you with them. Once a sizeable gap opens up a lot of folks ease up a bit and can't dig as deep so try not to give it away right at the bottom. You'll likely do a better job of keeping your head in the game if you stay with others till at least the midpoint of longer climbs and again this often means not downshifting into your easiest climbing cogs right at the base of the hill.
Lot's of technique and mental stuff to work on but all of that builds on top of solid sustainable power and total body plus bike plus kit weight. Keep working those Threshold intervals and hill repeats on your harder days, refuel but don't overfuel after workouts and keep working on the mental and technique aspects and your climbing will improve. But yes, don't ride hard rides seven days a week with no rest and not every ride needs to be Tempo or Threshold. But don't start avoiding the Tempo/Threshold sessions altogether as you're not going to get faster up medium to long climbs by riding Endurance pace all the time.
Good luck,
-Dave
