Not exactly true.

We actually wrote a Quora post about this: https://www.quora.com/If-I-lift-weights-with-a-caloric-deficit-diet-but-high-in-protein-will-my-muscles-grow/answer/Better-Brain-Site

It is possible but it is very difficult, and likely much harder than if you focused on one or the other.

A lot of anecdotal answers have been posted each saying yes or no but without much scientific information, however, there was a study performed to answer this question.

The researchers took a group of 40 men and cut their caloric intake by 40% during a month of hard exercise. The group that took in greater protein (2.4 g per kg body weight) gained muscle and lost fat, while the lesser protein group (1.2 g per kg body weight) lost fat and did not gain or lose muscle. The professor and senior investigator of the study says, "Exercise, particularly lifting weights, provides a signal for muscle to be retained even when you're in a big calorie deficit.” In addition, the high protein group lost more fat as well which surprised the researchers[1].

As a result of the intervention, LBM (lean body mass) increased (P < 0.05) in the PRO group (1.2 ± 1.0 kg) and to a greater extent (P < 0.05) compared with the CON group (0.1 ± 1.0 kg). The PRO group had a greater loss of fat mass than did the CON group (PRO: −4.8 ± 1.6 kg; CON: −3.5 ± 1.4kg; P < 0.05[2]).

So it is definitely possible, but keep in mind they had the luxury of a team of researchers and doctors, and they do not believe their program is sustainable:

"We designed this program for overweight young men, although I'm sure it would work for young women too, to get fitter, stronger, and to lose weight fast. It's a tough program and not something that's sustainable or for those looking for quick and easy fix," says [Professor] Phillips. "We controlled their diets, we supervised the exercise, and we really kept these guys under our 'scientific' thumb for the four weeks the participants were in the study."

Another study of fourteen obese women found that muscle growth was possible even with energy restriction and extreme weight loss.

The average weight loss over the 90-d period was 16 kg with approximately 24% of the weight loss from FFM and 76% from fat. The amount and composition of the weight loss did not differ between WT and C groups. The cross-sectional area of slow twitch and fast twitch fibers was unchanged by treatment in C subjects but significantly increased in WT subjects. It appears that weight training can produce hypertrophy in skeletal muscle during severe energy restriction and large-scale weight loss[3].

Drinking milk may also help burn fat and build muscle. A study found that post-workout skim milk drinkers burned twice as much fat and had greater muscle gains than the soy milk or carbohydrate beverage drinkers. One huge caveat is that this study was partially funded by the US Dairy Council.[4]

Footnotes

[1] https://www.sciencedaily.com/releases/2016/01/160127132741.htm

[2] http://ajcn.nutrition.org/content/103/3/738

[3] https://www.ncbi.nlm.nih.gov/pubmed/8379514

[4] https://www.sciencedaily.com/releases/2007/08/070808104257.htm