The USC webpage states
MARIJUANA USE CONSEQUENCES
The well-confirmed danger of smoking marijuana is lung damage and lung cancer. As examples:
1 joint = 5 cigarettes in terms of amount of carbon monoxide (CO) intake.
1 joint = 4 cigarettes in terms of amount of tar intake.
2 joints = 20 cigarettes in terms of microscopic damage to cells lining the airways.
These appear to be the only relevant numbers. This also appears to be where drugfreeworld gets their numbers for (emphasis added) "smoking one joint gives as much exposure to cancer-producing chemicals as smoking four to five cigarettes." drugfreeworld is likely generalizing CO and tar intake to cancer-producing chemicals.
While the USC webpage doesn't cite sources, a 2008 study wrote (emphasis added):
These factors are likely to be responsible for the five-fold greater absorption of carbon monoxide from a cannabis joint, compared with a tobacco cigarette of similar size despite similar carbon monoxide concentrations in the smoke inhaled.
Regarding tar, a 1998 study wrote (emphasis added):
To compare the pulmonary hazards of smoking marijuana and tobacco, we quantified the relative burden to the lung of insoluble particulates (tar) and carbon monoxide from the smoke of similar quantities of marijuana and tobacco. ...
As compared with smoking tobacco, smoking marijuana was associated with a nearly fivefold greater increment in the blood carboxyhemoglobin level, an approximately threefold increase in the amount of tar inhaled, and retention in the respiratory tract of one third more inhaled tar (P less than 0.001).
A 2008 paper writes:
These differential risks are greater than the 1:5 dose ratio between cannabis and tobacco for carbon monoxide levels and the 1:3 dose ratio for amount of tar inhaled.
This study cites the 1988 study for the 1:5 and 1:3 figures. This shows that the results of the 1988 study are still accepted in 2008. I couldn't find numbers from a more recent study.
A 2013 study wrote (emphasis added):
concern is heightened by the finding that the
smoke contents of marijuana and
a comparable quantity of tobacco (unfiltered
Kentucky reference cigarette) include roughly
similar amounts of volatile constituents
(including ammonia, hydrocyanic acid, and
nitrosamines) and qualitatively similar tar
components (including phenols, naphthalene,
and the procarcinogenic benzopyrene and
benzanthracene) with the major exceptions of nicotine (found only in tobacco) and [THC], the major psychoactive ingredient in marijuana, and
a number of other THC-like (cannabinoid)
compounds that are found only in marijuana.
Thus, the carcinogenic compounds in the tar are approximately the same for both marijuana and cigarettes. This means that exposure to more tar is proportionally related to exposure to more carcinogenic compounds.
Does smoking one joint give as much exposure to cancer-producing chemicals as smoking four to five cigarettes?
Smoking one joint gives as much exposure to carbon monoxide as smoking five cigarettes and as much exposure to tar as smoking three cigarettes. As the carcinogenic compounds in marijuana and cigarette tar are similar, smoking one joint gives as much exposure to cancer-producing chemicals as smoking three cigarettes. In this sense, the claim is slightly exaggerated. However, the claim may be misleading as exposure to cancer-producing chemicals (carcinogens) doesn't always directly relate to cancer risk.
A 2014 paper wrote (emphasis added):
Results from our pooled analyses provide little evidence for an increased risk of lung cancer among habitual or long‐term cannabis smokers, although the possibility of potential adverse effect for heavy consumption cannot be excluded.
A 2006 paper wrote (emphasis added):
Our results may have been affected by selection bias or error in measuring lifetime exposure and confounder histories; but they suggest that the association of [lung and upper aerodigestive tract] cancers with marijuana, even long-term or heavy use, is not strong and may be below practically detectable limits.
A 2005 paper wrote:
However, current knowledge does not suggest that cannabis smoke will have a carcinogenic potential comparable to that resulting from exposure to tobacco smoke.
The paper's conclusion explains why this is the case (partially because hydrocarbons in marijuana inhibit enzymes that convert carcinogen precursor compounds into carcinogenic compounds whereas nicotine activates these enzymes).
Thus, while marijuana may expose users to more tar and carbon monoxide, it does not necessarily increase cancer risk relative to tobacco.