Are presence questionnaires valid in a between-subjects design?
The underlying question here is: Does the context of a questionnaire affect the answer? 

I think you already answered the question yourself. Yes it does. 

Let's make the comparison even more extreme:


Please rate on a scale of 1 (not at all) to 7 (very) how happy you would be if you won 1 million dollars because you were the 1 millionth customer of a super market. 
Please rate on a scale of 1 (not at all) to 7 (very) how happy you would be to win 100 dollars because you were the 1 millionth customer of a super market. 


Now imagine you would have been asked only the second question. Will the answer on the second question be affected by the fact that there was question 1? Very likely.

For an excellent introduction to research about such context effects and other survey-related phenomena check out "Self-reports: How the questions shape the answers." by Norbert Schwarz (1999). 

Schwarz summarizes several ways in which pragmatic aspects of questions affect answers in questionnaires. There is an important distinction with regard to how people construct the meaning of such questions. On the one hand, there is the literal meaning of the question, its semantic content. On the other hand, there is also the pragmatic meaning of a question, which involves an assessment about the intention of the person (the researcher) who has asked the question. (What is implied? Also called the implicature). To infer this pragmatic meaning, people rely on several communication norms or "maxims" (Grice, 1975). 

The maxim that is most relevant here is the maxim of relation:


  a maxim of relation enjoins speakers to make their contribution
  relevant to the aims of the ongoing conversation. In research
  situations, this maxim licenses the use of contextual information in
  question interpretation and invites respondents to relate the question
  to the context of the ongoing exchange. (Schwarz, 1999, p. 94)


So in the context of question 1 (1 million dollars/presence in environment 1/2 liters of free beer), the pragmatic meaning of question 2 (100 dollars/presence in environment 2/1 liters of free beer) may be interpreted as comparative (compared to the first option, who much do you like it?) and the answer may be different that than when it is asked in isolation.

Another way in which the context may affect the answer is that the implied meaning of the scale anchors change (What means "very happy" vs. "not at all happy"?). An example of research that has investigated such issues is the research on shifting standards in stereotyping (e.g. Biernat &amp; Manis, 1994). For example, if you judge woman X with regard to aggressiveness, she may be rated as "highly aggressive" in the context of other women (because the stereotype is that women are low in aggressiveness). However, if the question is asked in the context of men, she might be rated lower in terms of aggressiveness (also because of the stereotype that women are less aggressive). The point is that the inferred meaning of the scale anchor "very aggressive" changes based on the context the question is asked in.  

References

Biernat, M., &amp; Manis, M. (1994). Shifting standards and stereotype-based judgments. Journal of Personality and Social Psychology, 66, 5–20. doi:10.1037/0022-3514.66.1.5

Grice, H. P. ( 1975). Logic and conversation. In P.Cole &amp; J. L.Morgan ( Eds.), Syntax and semantics: Vol. 3. Speech acts (pp. 41– 58). New York: Academic Press. 

Schwarz, N. (1999). Self-reports: How the questions shape the answers. American Psychologist, 54, 93–105. doi:10.1037/0003-066X.54.2.93